## Tian, Yongge

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 Author ID: tian.yongge Published as: Tian, Yongge; Tian, Y.; Tian, Yong Ge; Tian, Yong-ge; Tian, Yongee External Links: Google Scholar · ResearchGate · dblp
 Documents Indexed: 185 Publications since 1992 Co-Authors: 36 Co-Authors with 83 Joint Publications 916 Co-Co-Authors
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### Co-Authors

 98 single-authored 14 Jiang, Bo 12 Takane, Yoshio 11 Liu, Yonghui 10 Styan, George P. H. 6 Cheng, Shizhen 5 Sun, Yuqin 4 Lu, Changli 3 Guo, Wenxing 3 Herzberg, Agnes Margaret 3 Puntanen, Simo 3 Zhang, Xuan 2 Gan, Shengjun 2 Wang, Hongxing 2 Yanai, Haruo 1 Beisiegel, M. 1 Chuai, Jianjun 1 Dagenais, E. 1 Dong, Baomin 1 Gross, Jürgen 1 Haines, Christopher R. 1 Kala, Radosław 1 Ke, Rong 1 Li, Jing 1 Li, Shangzhi 1 Liu, Chunmei 1 Miao, S. F. 1 Qian, Hailong 1 Sun, Min 1 Tian, Zhe 1 von Rosen, Dietrich 1 Wang, Qingwen 1 Wang, Yufu 1 Wiens, Douglas P. 1 Xie, Pengyang 1 Zhang, Jieping 1 Zhang, Wei
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### Serials

 19 Linear and Multilinear Algebra 15 Linear Algebra and its Applications 9 ELA. The Electronic Journal of Linear Algebra 7 Applied Mathematics and Computation 6 Journal of Multivariate Analysis 6 Statistical Papers 5 Communications in Statistics. Theory and Methods 4 Metrika 4 Statistics & Probability Letters 4 Numerical Linear Algebra with Applications 4 Advances in Applied Clifford Algebras 3 Annals of the Institute of Statistical Mathematics 3 Journal of Statistical Planning and Inference 3 Southeast Asian Bulletin of Mathematics 3 Aequationes Mathematicae 3 Acta Mathematica Sinica. English Series 3 Open Mathematics 2 Computers & Mathematics with Applications 2 International Journal of Mathematical Education in Science and Technology 2 Journal of Mathematical Analysis and Applications 2 Beiträge zur Algebra und Geometrie 2 Archivum Mathematicum 2 Statistics 2 Acta Mathematica Universitatis Comenianae. New Series 2 Computational and Applied Mathematics 2 Journal of Inequalities and Applications 2 Mathematical Inequalities & Applications 2 Econometric Theory 2 Missouri Journal of Mathematical Sciences 2 Statistical Methods and Applications 2 Journal of the Korean Statistical Society 2 Journal of Mathematical Research with Applications 2 Special Matrices 1 Houston Journal of Mathematics 1 Journal of the Franklin Institute 1 Rocky Mountain Journal of Mathematics 1 Acta Scientiarum Mathematicarum 1 Calcolo 1 Commentationes Mathematicae Universitatis Carolinae 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Computational and Applied Mathematics 1 Journal of Mathematics of Kyoto University 1 Journal of Optimization Theory and Applications 1 Kyungpook Mathematical Journal 1 Mathematical Journal of Okayama University 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Publicationes Mathematicae 1 Rendiconti del Seminario Matematico della Università di Padova 1 Results in Mathematics 1 Journal of Mathematical Research & Exposition 1 Mathematics in Practice and Theory 1 Journal of Xiamen University. Natural Science 1 American Journal of Mathematical and Management Sciences 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Natural Science of Heilongjiang University 1 Computational Statistics 1 Algebras, Groups and Geometries 1 Computational Statistics and Data Analysis 1 Applied Mathematics 1 The New York Journal of Mathematics 1 Southwest Journal of Pure and Applied Mathematics 1 International Journal of Mathematics, Game Theory and Algebra 1 Revista Matemática Complutense 1 Scientiae Mathematicae Japonicae 1 International Mathematical Journal 1 Applied Mathematics E-Notes 1 Journal of Applied Mathematics and Computing 1 Central European Journal of Mathematics 1 Journal of Applied Algebra and Discrete Structures 1 Journal of Algebra and its Applications 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Mediterranean Journal of Mathematics 1 Journal of Concrete and Applicable Mathematics 1 Journal of Industrial and Management Optimization 1 Complex Analysis and Operator Theory 1 Acta Mathematica Sinica. Chinese Series 1 Operators and Matrices 1 Journal of Mathematical Inequalities 1 AStA. Advances in Statistical Analysis 1 Banach Journal of Mathematical Analysis 1 Annals of Functional Analysis 1 Numerical Algebra, Control and Optimization 1 Advances in Operator Theory
all top 5

### Fields

 148 Linear and multilinear algebra; matrix theory (15-XX) 58 Statistics (62-XX) 9 Operator theory (47-XX) 9 Numerical analysis (65-XX) 5 Operations research, mathematical programming (90-XX) 3 Associative rings and algebras (16-XX) 3 Nonassociative rings and algebras (17-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX)

### Citations contained in zbMATH Open

166 Publications have been cited 1,599 times in 532 Documents Cited by Year
Upper and lower bounds for ranks of matrix expressions using generalized inverses. Zbl 1016.15003
Tian, Yongge
2002
More on maximal and minimal ranks of Schur complements with applications. Zbl 1077.15005
Tian, Yongge
2004
Rank equalities for idempotent and involutory matrices. Zbl 0988.15002
Tian, Yongge; Styan, George P. H.
2001
Equalities and inequalities for inertias of Hermitian matrices with applications. Zbl 1205.15033
Tian, Yongge
2010
Reverse order laws for the generalized inverses of multiple matrix products. Zbl 0812.15002
Tian, Yongge
1994
The maximal and minimal ranks of some expressions of generalized inverses of matrices. Zbl 1007.15005
Tian, Yongge
2002
Extremal ranks of some symmetric matrix expressions with applications. Zbl 1123.15001
Tian, Yongge; Liu, Yonghui
2006
The maximal and minimal ranks of $$A - BXC$$ with applications. Zbl 1036.15004
Tian, Yongge; Cheng, Shizhen
2003
The solvability of two linear matrix equations. Zbl 0970.15005
Tian, Yongge
2000
Max-min problems on the ranks and inertias of the matrix expressions $$A - BXC \pm (BXC)^{\ast}$$ with applications. Zbl 1223.90077
Liu, Yonghui; Tian, Yongge
2011
Maximization and minimization of the rank and inertia of the Hermitian matrix expression $$A-BX-(BX)^{*}$$ with applications. Zbl 1211.15022
Tian, Yongge
2011
Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix products. Zbl 1037.15003
Tian, Yongge
2004
More on extremal ranks of the matrix expressions $$A-BX \pm X^{*}B^{*}$$ with statistical applications. Zbl 1212.15029
Liu, Y.; Tian, Y.
2008
Matrix representations of octonions and their applications. Zbl 0974.15012
Tian, Yongge
2000
Ranks of solutions of the matrix equation $$AXB=C$$. Zbl 1040.15003
Tian, Yongge
2002
On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model. Zbl 1123.62038
Tian, Yongge; Wiens, Douglas P.
2006
Ranks of Hermitian and skew-Hermitian solutions to the matrix equation $$AXA^*=B$$. Zbl 1180.15018
Liu, Yonghui; Tian, Yongge; Takane, Yoshio
2009
On the natural restrictions in the singular Gauss-Markov model. Zbl 1148.62053
Tian, Yongge; Beisiegel, M.; Dagenais, E.; Haines, C.
2008
A simultaneous decomposition of a matrix triplet with applications. Zbl 1249.15020
Liu, Yonghui; Tian, Yongge
2011
The Moore-Penrose inverses of $$m\times n$$ block matrices and their applications. Zbl 0932.15004
Tian, Yongge
1998
Two sets of new characterizations for normal and EP matrices. Zbl 1054.15022
Cheng, Shizhen; Tian, Yongge
2003
A new derivation of BLUPs under random-effects model. Zbl 1329.62264
Tian, Yongge
2015
The minimum rank of a $$3\times 3$$ partial block matrix. Zbl 1006.15004
Tian, Yongge
2002
On sum decompositions of weighted least-squares estimators for the partitioned linear model. Zbl 1139.62029
Tian, Yongge; Takane, Yoshio
2008
On an additive decomposition of the BLUE in a multiple-partitioned linear model. Zbl 1155.62045
Tian, Yongge
2009
On mixed-type reverse-order laws for the Moore-Penrose inverse of a matrix product. Zbl 1075.15011
Tian, Yongge
2004
On the equivalence of estimations under a general linear model and its transformed models. Zbl 1160.62330
Tian, Yongge; Puntanen, Simo
2009
On equalities of estimations of parametric functions under a general linear model and its restricted models. Zbl 1197.62020
Tian, Yongge
2010
Completing triangular block matrices with maximal and minimal ranks. Zbl 0984.15013
Tian, Yongge
2000
Rank equalities related to outer inverses of matrices and applications. Zbl 0992.15004
Tian, Yongge
2001
Extremal ranks of submatrices in an Hermitian solution to the matrix equation $$AXA^{*}=B$$ with applications. Zbl 1194.15014
Liu, Yonghui; Tian, Yongge
2010
On consistency, natural restrictions and estimability under classical and extended growth curve models. Zbl 1160.62051
Tian, Yongge; Takane, Yoshio
2009
A matrix handling of predictions of new observations under a general random-effects model. Zbl 1329.62321
Tian, Yongge
2015
Characterizations of EP matrices and weighted-EP matrices. Zbl 1209.15039
Tian, Yongge; Wang, Hongxing
2011
How to characterize equalities for the Moore-Penrose inverse of a matrix. Zbl 0987.15001
Tian, Yongge
2001
The Moore-Penrose inverse of a triple matrix product. Zbl 0786.15009
Tian, Yongge
1992
Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method. Zbl 1236.65070
Tian, Yongge
2012
Three rank formulas associated with the covariance matrices of the BLUE and the OLSE in the general linear model. Zbl 1072.62049
Puntanen, Simo; Styan, George P. H.; Tian, Yongge
2005
Some properties of projectors associated with the WLSE under a general linear model. Zbl 1141.62043
Tian, Yongge; Takane, Yoshio
2008
Rank equalities for block matrices and their Moore-Penrose inverses. Zbl 1057.15006
Tian, Yongge
2004
On $$\mathbf V$$-orthogonal projectors associated with a semi-norm. Zbl 1332.15016
Tian, Yongge; Takane, Yoshio
2009
Some identities for Moore-Penrose inverses of matrix products. Zbl 1070.15003
Tian, Yongge; Cheng, Shizhen
2004
The equivalence between $$(AB)^\dagger=B^\dagger{}A^\dagger$$ and other mixed-type reverse-order laws. Zbl 1274.15019
Tian, Yongge
2006
On relations between BLUEs under two transformed linear models. Zbl 1299.62055
Dong, Baomin; Guo, Wenxing; Tian, Yongge
2014
Similarity and consimilarity of elements in the real Cayley-Dickson algebras. Zbl 1043.17500
Tian, Yongge
1999
Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications. Zbl 1252.15026
Tian, Yongge
2012
Completing block Hermitian matrices with maximal and minimal ranks and inertias. Zbl 1207.15029
Tian, Yongge
2010
Moore-Penrose inverses of products and differences of orthogonal projectors. Zbl 1052.15006
Cheng, Shizen; Tian, Yongge
2003
More on generalized inverses of partitioned matrices with Banachiewicz-Schur forms. Zbl 1162.15002
Tian, Yongge; Takane, Yoshio
2009
Universal similarity factorization equalities over real Clifford algebras. Zbl 0926.15026
Tian, Yongge
1998
An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices. Zbl 1358.15012
Tian, Yongge; Jiang, Bo
2016
Extremal ranks of a quadratic matrix expression with applications. Zbl 1220.15006
Tian, Yongge
2011
Some equalities for estimations of partial coefficients under a general linear regression model. Zbl 1229.62075
Tian, Yongge; Zhang, Jieping
2011
Solutions to 18 constrained optimization problems on the rank and inertia of the linear matrix function. Zbl 1255.15010
Tian, Yongge
2012
Invariance properties of a triple matrix product involving generalized inverses. Zbl 1105.15005
Groß, Jürgen; Tian, Yongge
2006
Rank equalities for idempotent matrices with applications. Zbl 1095.15002
Tian, Yongge; Styan, George P. H.
2006
Partially superfluous observations. Zbl 1125.62069
Qian, Hailong; Tian, Yongge
2006
On equalities for BLUEs under misspecified Gauss-Markov models. Zbl 1180.62083
Tian, Yong Ge
2009
On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product. Zbl 1125.15006
Takane, Yoshio; Tian, Yongge; Yanai, Haruo
2007
Two universal similarity factorization equalities for commutative involutory and idempotent matrices and their applications. Zbl 1256.15007
Tian, Yongge
2011
Some algebraic and statistical properties of {WLSE}s under a general growth curve model. Zbl 1152.62349
Tian, Yongge; Takane, Yoshio
2007
Cochran’s statistical theorem revisited. Zbl 1094.15003
Tian, Yongge; Styan, George P. H.
2006
The minimal rank of the matrix expression $$A-BX-YC$$. Zbl 1032.15001
Tian, Yongge
2002
Equivalence of predictors under real and over-parameterized linear models. Zbl 1369.62118
Gan, Shengjun; Sun, Yuqin; Tian, Yongge
2017
The inverse of any two-by-two nonsingular partitioned matrix and three matrix inverse completion problems. Zbl 1186.15005
Tian, Yongge; Takane, Yoshio
2009
Some remarks on general linear model with new regressors. Zbl 1312.62091
Lu, Changli; Gan, Shengjun; Tian, Yongge
2015
How to establish universal block-matrix factorizations. Zbl 0979.15012
Tian, Yongge; Styan, George P. H.
2001
Some notes on linear sufficiency. Zbl 1357.62240
Kala, Radosław; Puntanen, Simo; Tian, Yongge
2017
Matrix rank and inertia formulas in the analysis of general linear models. Zbl 1359.15003
Tian, Yongge
2017
Some equalities and inequalities for covariance matrices of estimators under linear model. Zbl 1365.62207
Tian, Y.
2017
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix. Zbl 1207.15007
Tian, Yongge
2010
Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors. Zbl 1217.15015
Tian, Yongge
2011
Relations between least-squares and least-rank solutions of the matrix equation $$AXB=C$$. Zbl 1293.15012
Tian, Yongge; Wang, Hongxing
2013
Universal factorization equalities for quaternion matrices and their applications. Zbl 0979.15011
Tian, Yongge
1999
Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions. Zbl 1278.15019
Tian, Yongge
2014
Cochran’s statistical theorem for outer inverses of matrices and matrix quadratic forms. Zbl 1083.15007
Tian, Yongge; Styan, George P. H.
2005
How to express a parallel sum of $$k$$ matrices. Zbl 0997.15004
Tian, Yongge
2002
Some properties of submatrices in a solution to the matrix equation $$AXB=C$$ with applications. Zbl 1168.15307
Tian, Yongge
2009
A-minimax and D-minimax robust optimal designs for approximately linear Haar-wavelet models. Zbl 1445.62204
Tian, Yongge; Herzberg, Agnes M.
2006
A new rank formula for idempotent matrices with applications. Zbl 1090.15001
Tian, Yongge; Styan, George P. H.
2002
Estimation and optimal designs for linear Haar-wavelet models. Zbl 1433.62221
Tian, Yongge; Herzberg, Agnes M.
2007
Equalities for estimators of partial parameters under linear model with restrictions. Zbl 1328.62347
Tian, Yongge; Jiang, Bo
2016
On decompositions of BLUEs under a partitioned linear model with restrictions. Zbl 1341.62142
Zhang, Xuan; Tian, Yongge
2016
Estimations of parametric functions under a system of linear regression equations with correlated errors. Zbl 1197.62062
Tian, Yong Ge
2010
Two competing linear random-effects models and their connections. Zbl 1401.62111
Lu, Changli; Sun, Yuqin; Tian, Yongge
2018
A survey on rank and inertia optimization problems of the matrix-valued function $$A+BXB^\ast$$. Zbl 1327.15007
Tian, Yongge
2015
Characterizing relationships between estimations under a general linear model with explicit and implicit restrictions by rank of matrix. Zbl 1271.62152
Tian, Yongge
2012
On additive and block decompositions of WLSEs under a multiple partitioned regression model. Zbl 1283.62146
Tian, Yongge; Tian, Zhe
2010
On properties of BLUEs under general linear regression models. Zbl 1428.62344
Tian, Yongge
2013
Rank equalities and inequalities for Kronecker products of matrices with applications. Zbl 1041.15016
Chuai, Jianjun; Tian, Yongge
2004
Some mixed-type reverse-order laws for the Moore-Penrose inverse of a triple matrix product. Zbl 1152.15007
Tian, Yongge
2007
Schur complements and Banachiewicz-Schur forms. Zbl 1095.15006
Tian, Yongge; Takane, Yoshio
2005
The reverse-order law $$(AB)^\dagger= B^\dagger (A^\dagger ABB^\dagger)^\dagger A^\dagger$$ and its equivalent equalities. Zbl 1099.15004
Tian, Yongge
2005
Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications. Zbl 1344.15003
Tian, Yongge
2016
Solutions of a constrained Hermitian matrix-valued function optimization problem with applications. Zbl 1357.65079
Tian, Yongge
2016
A new analysis of the relationships between a general linear model and its mis-specified forms. Zbl 1362.62143
Tian, Yongge; Jiang, Bo
2017
On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model. Zbl 1341.62133
Tian, Yongge; Zhang, Xuan
2016
The Moore-Penrose inverse for sums of matrices under rank additivity conditions. Zbl 1076.15008
Tian, Yongge
2005
Closed-form formulas for calculating the max-min ranks of a triple matrix product composed by generalized inverses. Zbl 1413.15002
Tian, Yongge; Jiang, Bo
2018
Least-squares solutions and least-rank solutions of the matrix equation $$AXA^{*}=B$$ and their relations. Zbl 1313.65095
Tian, Yongge
2013
Two groups of mixed reverse order laws for generalized inverses of two and three matrix products. Zbl 1449.15005
Tian, Yongge
2020
Miscellaneous reverse order laws for generalized inverses of matrix products with applications. Zbl 1446.15003
Tian, Yongge
2020
Necessary and sufficient conditions for nonlinear matrix identities to always hold. Zbl 1414.15022
Jiang, Bo; Tian, Yongge
2019
On relationships between two linear subspaces and two orthogonal projectors. Zbl 1433.15005
Tian, Yongge
2019
Formulas for calculating the dimensions of the sums and the intersections of a family of linear subspaces with applications. Zbl 1425.15001
Tian, Yongge
2019
Two competing linear random-effects models and their connections. Zbl 1401.62111
Lu, Changli; Sun, Yuqin; Tian, Yongge
2018
Closed-form formulas for calculating the max-min ranks of a triple matrix product composed by generalized inverses. Zbl 1413.15002
Tian, Yongge; Jiang, Bo
2018
How to establish exact formulas for calculating the max-min ranks of products of two matrices and their generalized inverses. Zbl 1386.15007
Tian, Yongge
2018
A comparison between two competing fixed parameter constrained general linear models with new regressors. Zbl 1395.62126
Lu, Changli; Sun, Yuqin; Tian, Yongge
2018
Equivalence of predictors under real and over-parameterized linear models. Zbl 1369.62118
Gan, Shengjun; Sun, Yuqin; Tian, Yongge
2017
Some notes on linear sufficiency. Zbl 1357.62240
Kala, Radosław; Puntanen, Simo; Tian, Yongge
2017
Matrix rank and inertia formulas in the analysis of general linear models. Zbl 1359.15003
Tian, Yongge
2017
Some equalities and inequalities for covariance matrices of estimators under linear model. Zbl 1365.62207
Tian, Y.
2017
A new analysis of the relationships between a general linear model and its mis-specified forms. Zbl 1362.62143
Tian, Yongge; Jiang, Bo
2017
Decomposition of approaches of a general linear model with fixed parameters. Zbl 1381.62102
Jiang, Bo; Tian, Yongge
2017
On decompositions of estimators under a general linear model with partial parameter restrictions. Zbl 06819962
Jiang, Bo; Tian, Yongge; Zhang, Xuan
2017
Transformation approaches of linear random-effects models. Zbl 1441.62147
Tian, Yongge
2017
On additive decompositions of estimators under a multivariate general linear model and its two submodels. Zbl 1403.62100
Jiang, Bo; Tian, Yongge
2017
On simultaneous prediction in a multivariate general linear model with future observations. Zbl 1373.62263
Tian, Yongge; Wang, Cheng
2017
Quadratic properties of least-squares solutions of linear matrix equations with statistical applications. Zbl 1417.15018
Tian, Yongge; Jiang, Bo
2017
On equivalence of predictors/estimators under a multivariate general linear model with augmentation. Zbl 1377.62143
Jiang, Bo; Tian, Yongge
2017
Rank/inertia approaches to weighted least-squares solutions of linear matrix equations. Zbl 1426.15020
Jiang, Bo; Tian, Yongge
2017
Upper and lower bounds for the rank of the matrix-valued function $$A+BXC$$ when $$X$$ has a fixed rank. Zbl 1387.15013
Tian, Yongge
2017
An algebraic study of BLUPs under two linear random-effects models with correlated covariance matrices. Zbl 1358.15012
Tian, Yongge; Jiang, Bo
2016
Equalities for estimators of partial parameters under linear model with restrictions. Zbl 1328.62347
Tian, Yongge; Jiang, Bo
2016
On decompositions of BLUEs under a partitioned linear model with restrictions. Zbl 1341.62142
Zhang, Xuan; Tian, Yongge
2016
Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications. Zbl 1344.15003
Tian, Yongge
2016
Solutions of a constrained Hermitian matrix-valued function optimization problem with applications. Zbl 1357.65079
Tian, Yongge
2016
On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model. Zbl 1341.62133
Tian, Yongge; Zhang, Xuan
2016
On comparison of dispersion matrices of estimators under a constrained linear model. Zbl 1392.62209
Tian, Yongge; Guo, Wenxing
2016
Matrix rank/inertia formulas for least-squares solutions with statistical applications. Zbl 1333.15006
Tian, Yongge; Jiang, Bo
2016
A new derivation of BLUPs under random-effects model. Zbl 1329.62264
Tian, Yongge
2015
A matrix handling of predictions of new observations under a general random-effects model. Zbl 1329.62321
Tian, Yongge
2015
Some remarks on general linear model with new regressors. Zbl 1312.62091
Lu, Changli; Gan, Shengjun; Tian, Yongge
2015
A survey on rank and inertia optimization problems of the matrix-valued function $$A+BXB^\ast$$. Zbl 1327.15007
Tian, Yongge
2015
On relations between BLUEs under two transformed linear models. Zbl 1299.62055
Dong, Baomin; Guo, Wenxing; Tian, Yongge
2014
Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions. Zbl 1278.15019
Tian, Yongge
2014
Some overall properties of seemingly unrelated regression models. Zbl 1443.62206
Sun, Yuqin; Ke, Rong; Tian, Yongge
2014
On relations among solutions of the Hermitian matrix equation $$AXA^* = B$$ and its three small equations. Zbl 1296.15009
Li, Ying; Tian, Yongge
2014
How to solve three fundamental linear matrix inequalities in the Löwner partial ordering. Zbl 1297.15024
Tian, Yongge
2014
Expansion formulas for orthogonal projectors onto ranges of row block matrices. Zbl 1313.15004
Tian, Yongge; Wang, Yufu
2014
Relations between least-squares and least-rank solutions of the matrix equation $$AXB=C$$. Zbl 1293.15012
Tian, Yongge; Wang, Hongxing
2013
On properties of BLUEs under general linear regression models. Zbl 1428.62344
Tian, Yongge
2013
Least-squares solutions and least-rank solutions of the matrix equation $$AXA^{*}=B$$ and their relations. Zbl 1313.65095
Tian, Yongge
2013
Hermitian-type generalized singular value decomposition with applications. Zbl 1289.65108
Liu, Yonghui; Tian, Yongge
2013
On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models. Zbl 1307.62180
Lu, Changli; Sun, Yuqin; Tian, Yongge
2013
Equalities and inequalities for Hermitian solutions and Hermitian definite solutions of the two matrix equations $$AX = B$$ and $$AXA ^{*} = B$$. Zbl 1281.15016
Tian, Yongge
2013
Biquaternions and their complex matrix representations. Zbl 1280.15011
Tian, Yongge
2013
Solutions of the matrix inequalities in the minus partial ordering and Löwner partial ordering. Zbl 1273.15002
Tian, Yongge
2013
Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method. Zbl 1236.65070
Tian, Yongge
2012
Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications. Zbl 1252.15026
Tian, Yongge
2012
Solutions to 18 constrained optimization problems on the rank and inertia of the linear matrix function. Zbl 1255.15010
Tian, Yongge
2012
Characterizing relationships between estimations under a general linear model with explicit and implicit restrictions by rank of matrix. Zbl 1271.62152
Tian, Yongge
2012
On additive decomposition of the Hermitian solution of the matrix equation $$AXA^* = B$$. Zbl 1241.15012
Tian, Yongge
2012
Distributions of eigenvalues and inertias of some block Hermitian matrices consisting of orthogonal projectors. Zbl 1261.15013
Tian, Yongge; Li, Ying
2012
Bifurcation set and number of limit cycles in $$Z_{2}$$-equivariant planar vector fields of degree 5. Zbl 1243.37043
Li, J.; Zhang, W.; Miao, S. F.; Sun, M.; Tian, Y.
2012
Solving the matrix inequality $$AXB + (AXB)^{*} \geqslant C$$. Zbl 1246.15008
Tian, Yongge; Von Rosen, Dietrich
2012
Max-min problems on the ranks and inertias of the matrix expressions $$A - BXC \pm (BXC)^{\ast}$$ with applications. Zbl 1223.90077
Liu, Yonghui; Tian, Yongge
2011
Maximization and minimization of the rank and inertia of the Hermitian matrix expression $$A-BX-(BX)^{*}$$ with applications. Zbl 1211.15022
Tian, Yongge
2011
A simultaneous decomposition of a matrix triplet with applications. Zbl 1249.15020
Liu, Yonghui; Tian, Yongge
2011
Characterizations of EP matrices and weighted-EP matrices. Zbl 1209.15039
Tian, Yongge; Wang, Hongxing
2011
Extremal ranks of a quadratic matrix expression with applications. Zbl 1220.15006
Tian, Yongge
2011
Some equalities for estimations of partial coefficients under a general linear regression model. Zbl 1229.62075
Tian, Yongge; Zhang, Jieping
2011
Two universal similarity factorization equalities for commutative involutory and idempotent matrices and their applications. Zbl 1256.15007
Tian, Yongge
2011
Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors. Zbl 1217.15015
Tian, Yongge
2011
A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications. Zbl 1235.15007
Tian, Yongge
2011
Solving a minus partial ordering equation over von Neumann regular rings. Zbl 1230.16011
Tian, Yongge
2011
Relations between matrix sets generated from linear matrix expressions and their applications. Zbl 1217.15021
Tian, Yongge
2011
Equalities and inequalities for inertias of Hermitian matrices with applications. Zbl 1205.15033
Tian, Yongge
2010
On equalities of estimations of parametric functions under a general linear model and its restricted models. Zbl 1197.62020
Tian, Yongge
2010
Extremal ranks of submatrices in an Hermitian solution to the matrix equation $$AXA^{*}=B$$ with applications. Zbl 1194.15014
Liu, Yonghui; Tian, Yongge
2010
Completing block Hermitian matrices with maximal and minimal ranks and inertias. Zbl 1207.15029
Tian, Yongge
2010
Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix. Zbl 1207.15007
Tian, Yongge
2010
Estimations of parametric functions under a system of linear regression equations with correlated errors. Zbl 1197.62062
Tian, Yong Ge
2010
On additive and block decompositions of WLSEs under a multiple partitioned regression model. Zbl 1283.62146
Tian, Yongge; Tian, Zhe
2010
Equalities for orthogonal projectors and their operations. Zbl 1223.15010
Tian, Yongge
2010
Weighted least-squares estimators of parametric functions of the regression coefficients under a general linear model. Zbl 1432.62214
Tian, Yongge
2010
On additive decompositions of solutions of the matrix equation $$AXB=C$$. Zbl 1214.15009
Tian, Yongge
2010
How to use RSVD to solve the matrix equation $$A=BXC$$. Zbl 1202.15019
Liu, Yonghui; Tian, Yongge
2010
Solving two pairs of quadratic equations in quaternions. Zbl 1188.15015
Tian, Yongge
2010
Eight expressions for generalized inverses of a bordered matrix. Zbl 1188.15006
Tian, Yongge
2010
Solving some linear equations over alternative rings. Zbl 1201.17019
Tian, Yongge
2010
Some equalities for estimations of variance components in a general linear model and its restricted and transformed models. Zbl 1203.62107
Tian, Yongge; Liu, Chunmei
2010
Ranks of Hermitian and skew-Hermitian solutions to the matrix equation $$AXA^*=B$$. Zbl 1180.15018
Liu, Yonghui; Tian, Yongge; Takane, Yoshio
2009
On an additive decomposition of the BLUE in a multiple-partitioned linear model. Zbl 1155.62045
Tian, Yongge
2009
On the equivalence of estimations under a general linear model and its transformed models. Zbl 1160.62330
Tian, Yongge; Puntanen, Simo
2009
On consistency, natural restrictions and estimability under classical and extended growth curve models. Zbl 1160.62051
Tian, Yongge; Takane, Yoshio
2009
On $$\mathbf V$$-orthogonal projectors associated with a semi-norm. Zbl 1332.15016
Tian, Yongge; Takane, Yoshio
2009
More on generalized inverses of partitioned matrices with Banachiewicz-Schur forms. Zbl 1162.15002
Tian, Yongge; Takane, Yoshio
2009
On equalities for BLUEs under misspecified Gauss-Markov models. Zbl 1180.62083
Tian, Yong Ge
2009
The inverse of any two-by-two nonsingular partitioned matrix and three matrix inverse completion problems. Zbl 1186.15005
Tian, Yongge; Takane, Yoshio
2009
Some properties of submatrices in a solution to the matrix equation $$AXB=C$$ with applications. Zbl 1168.15307
Tian, Yongge
2009
Estimations and optimal designs for two-dimensional Haar-wavelet regression models. Zbl 1170.62056
Tian, Yongge
2009
On some matrix equalities for generalized inverses with applications. Zbl 1165.15006
Tian, Yongge; Styan, George P. H.
2009
A mixed-type reverse order law for generalized inverse of a triple matrix product. Zbl 1199.15021
Liu, Yonghui; Tian, Yongge
2009
More on extremal ranks of the matrix expressions $$A-BX \pm X^{*}B^{*}$$ with statistical applications. Zbl 1212.15029
Liu, Y.; Tian, Y.
2008
On the natural restrictions in the singular Gauss-Markov model. Zbl 1148.62053
Tian, Yongge; Beisiegel, M.; Dagenais, E.; Haines, C.
2008
On sum decompositions of weighted least-squares estimators for the partitioned linear model. Zbl 1139.62029
Tian, Yongge; Takane, Yoshio
2008
Some properties of projectors associated with the WLSE under a general linear model. Zbl 1141.62043
Tian, Yongge; Takane, Yoshio
2008
On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product. Zbl 1125.15006
Takane, Yoshio; Tian, Yongge; Yanai, Haruo
2007
...and 66 more Documents
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### Cited by 453 Authors

 119 Tian, Yongge 42 Wang, Qingwen 23 Đorđević, Dragan S. 23 Mosić, Dijana 20 Xiong, Zhiping 18 Cvetković-Ilić, Dragana S. 17 Deng, Chunyuan 16 Liu, Yonghui 15 Jiang, Bo 15 Song, Guangjing 14 Baksalary, Oskar Maria 13 Takane, Yoshio 13 Trenkler, Götz 13 Yu, Shaowen 11 Liu, Xiaoji 11 Puntanen, Simo 11 Wang, Hongxing 10 He, ZhuoHeng 10 Qin, Yingying 8 Guo, Wenbin 8 Zheng, Bing 7 Lin, Chunyan 7 Liu, Xifu 7 Wei, Musheng 6 Benítez Lopez, Julio 6 Dinčić, Nebojša Č. 6 Liu, Xin 6 Markiewicz, Augustyn 6 Song, Youngkwon 6 Styan, George P. H. 6 Sun, Yuqin 6 Wei, Yimin 5 Chang, Haixia 5 Chen, Jianlong 5 Koliha, Jerry J. 5 Li, Ying 5 Liu, Lina 4 Kyrchei, Ivan I. 4 Lee, Doohann 4 Liu, Zhongshan 4 Lu, Changli 4 Rakočević, Vladimir 4 Shpakivskyi, Vitalii Stanislavovich 4 Stanimirović, Predrag S. 4 Thome, Néstor 4 Yang, Hu 4 Yuan, Yongxin 4 Zhang, Fengxia 4 Zhang, Huiting 4 Zhao, Jianli 3 Cohen, Nir 3 Demir, Süleyman 3 Flaut, Cristina 3 Guterman, Alexander Èmilevich 3 Katsikis, Vasilios N. 3 Liao, Anping 3 Liu, Hao 3 Nikolov, Jovana 3 Pappas, Dimitrios 3 Patrício, Pedro 3 Pavlović, Vladimir 3 Pereira, Edgar 3 Ren, Xingwei 3 Tosun, Murat 3 Wang, Guorong 3 Wu, Zhongcheng 3 Yu, Yaoming 3 Zhang, Xuan 2 Akkus, Ilker 2 Beasley, LeRoy B. 2 Behera, Ratikanta 2 Benard, Emmanuel 2 Boasso, Enrico 2 Chen, Guoliang 2 Chen, Ming 2 Cheng, Shizhen 2 Dai, Lifang 2 Farid, Farid O. 2 Feng, Jun’e 2 Gowda, Muddappa Seetharama 2 Güler, Nesrin 2 Guo, Wenxing 2 Hajarian, Masoud 2 Haslett, Stephen J. 2 Hauke, Jan 2 Hernández, Araceli 2 Hou, Jian 2 Huang, Ting-Zhu 2 Huang, Yunying 2 Isotalo, Jarkko 2 Jin, Hongwei 2 Kala, Radosław 2 Keçilioğlu, Osman 2 Kolundžija, Milica Z. 2 Kösal, Hidayet Hüda 2 Krishnaswamy, D. 2 Lattanzi, Marina Beatriz 2 Li, Yuan 2 Liang, Hanying 2 Liang, Maolin ...and 353 more Authors
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### Cited in 115 Serials

 73 Applied Mathematics and Computation 67 Linear Algebra and its Applications 61 Linear and Multilinear Algebra 16 Advances in Applied Clifford Algebras 12 Computers & Mathematics with Applications 12 Journal of Mathematical Analysis and Applications 12 Statistical Papers 10 Journal of Multivariate Analysis 10 Computational and Applied Mathematics 9 Aequationes Mathematicae 9 Communications in Statistics. Theory and Methods 9 Journal of Applied Mathematics and Computing 8 Algebra Colloquium 7 Journal of the Franklin Institute 7 Journal of Computational and Applied Mathematics 7 Abstract and Applied Analysis 6 Statistics & Probability Letters 6 Mediterranean Journal of Mathematics 6 Banach Journal of Mathematical Analysis 6 Open Mathematics 5 Computational Statistics and Data Analysis 5 Numerical Linear Algebra with Applications 5 Journal of Inequalities and Applications 5 Acta Mathematica Sinica. English Series 5 Journal of Applied Mathematics 4 Communications in Algebra 4 Annals of the Institute of Statistical Mathematics 4 Journal of Statistical Planning and Inference 4 International Journal of Wavelets, Multiresolution and Information Processing 4 Complex Analysis and Operator Theory 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 Special Matrices 4 AIMS Mathematics 3 International Journal of Mathematical Education in Science and Technology 3 Indian Journal of Pure & Applied Mathematics 3 Applied Mathematics Letters 3 Filomat 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Journal of the Korean Statistical Society 3 Operators and Matrices 2 International Journal of Theoretical Physics 2 Metrika 2 Rocky Mountain Journal of Mathematics 2 Beiträge zur Algebra und Geometrie 2 Automatica 2 Calcolo 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Optimization Theory and Applications 2 Numerical Functional Analysis and Optimization 2 Statistics 2 International Journal of Computer Mathematics 2 Multibody System Dynamics 2 Journal of Shanghai University 2 Central European Journal of Mathematics 2 Statistical Methods and Applications 2 Journal of Industrial and Management Optimization 2 Journal of Statistical Theory and Practice 2 Science China. Mathematics 2 Numerical Algebra, Control and Optimization 2 Journal of Linear and Topological Algebra 1 International Journal of Modern Physics A 1 Inverse Problems 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Theoretical and Mathematical Physics 1 Mathematics of Computation 1 The Annals of Statistics 1 Matematički Vesnik 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matematico della Università di Padova 1 Revista de la Unión Matemática Argentina 1 Semigroup Forum 1 Probability and Mathematical Statistics 1 American Journal of Mathematical and Management Sciences 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Symbolic Computation 1 Facta Universitatis. Series Mathematics and Informatics 1 Mathematical and Computer Modelling 1 Neural Networks 1 Machine Learning 1 Numerical Algorithms 1 Computational Statistics 1 Communications in Statistics. Simulation and Computation 1 Journal of Mathematical Sciences (New York) 1 Journal of the Egyptian Mathematical Society 1 Turkish Journal of Mathematics 1 Random Operators and Stochastic Equations 1 ELA. The Electronic Journal of Linear Algebra 1 Mathematical Problems in Engineering 1 Differential Equations and Dynamical Systems 1 Nonlinear Dynamics 1 Revista Matemática Complutense 1 Communications of the Korean Mathematical Society 1 Acta et Commentationes Universitatis Tartuensis de Mathematica 1 Econometric Theory 1 Applied Stochastic Models in Business and Industry 1 Journal of the Australian Mathematical Society 1 Journal of Algebra and its Applications 1 Computational Biology and Chemistry 1 Advances in Difference Equations ...and 15 more Serials
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### Cited in 37 Fields

 390 Linear and multilinear algebra; matrix theory (15-XX) 101 Statistics (62-XX) 76 Operator theory (47-XX) 63 Numerical analysis (65-XX) 34 Associative rings and algebras (16-XX) 29 Functional analysis (46-XX) 12 Number theory (11-XX) 10 Nonassociative rings and algebras (17-XX) 10 Operations research, mathematical programming (90-XX) 6 Combinatorics (05-XX) 6 Probability theory and stochastic processes (60-XX) 6 Systems theory; control (93-XX) 5 Functions of a complex variable (30-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Mechanics of particles and systems (70-XX) 3 Partial differential equations (35-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 3 Biology and other natural sciences (92-XX) 2 Field theory and polynomials (12-XX) 2 Group theory and generalizations (20-XX) 2 Difference and functional equations (39-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 2 Relativity and gravitational theory (83-XX) 2 Information and communication theory, circuits (94-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)