×

zbMATH — the first resource for mathematics

The growth of powers of a nonnegative matrix. (English) Zbl 0498.65018

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
PDF BibTeX Cite
Full Text: DOI
References:
[1] Berman, Abraham; Plemmons, RobertJ., Nonnegative matrices in the mathematical sciences, (1979) · Zbl 0484.15016
[2] Brualdi, RichardA., Introductory combinatorics, (1977) · Zbl 0385.05001
[3] Carlson, D. H., A note on M-matrix equations, J. Soc. Indust. Appl. Math., 11, 1027, (1963) · Zbl 0196.30202
[4] Collatz, L., Einschliessungssatz für die charakteristischen zahlen von matrizen, Math. Z., 48, 221, (1942) · Zbl 0027.00604
[5] Friedland, Shmuel, On an inverse problem for nonnegative and eventually nonnegative matrices, Israel J. Math., 29, 43, (1978) · Zbl 0407.15015
[6] Frobenius, G. F., Über matrizen aus nicht negativen elementen, S. B. Kön. Preuss. Akad. Wiss. Berlin, 456, (1912) · JFM 43.0204.09
[7] Gantmacher, F. R., The Theory of Matrices, (1959) · Zbl 0085.01001
[8] Hardy, G. H., Divergent Series, (1949) · Zbl 0032.05801
[9] Karlin, Samuel, Positive operators, J. Math. Mech., 8, 907, (1959) · Zbl 0087.11002
[10] Meyer, C. D.; Plemmons, R. J., Convergent powers of a matrix with applications to iterative methods for singular linear systems, SIAM J. Numer. Anal., 14, 699, (1977) · Zbl 0366.65017
[11] Ostrowski, A., Über die determinanten mit überwiegender hauptdiagonale, Comment. Math. Helv., 10, 69, (1937) · Zbl 0017.29010
[12] Richman, D.; Schneider, H., On the singular graph and the Weyr characteristic of an M-matrix, Aequationes Math., 17, 208, (1978) · Zbl 0379.15009
[13] Rothblum, UrielG., Algebraic eigenspaces of nonnegative matrices, Linear Algebra and Appl., 12, 281, (1975) · Zbl 0321.15010
[14] Rothblum, UrielG., Expansions of sums of matrix powers, SIAM Rev., 23, 143, (1981) · Zbl 0466.15005
[15] Sensitive growth analysis of multiplicative systems I: the dynamic approachYale Univ. Rep., New Haven, CT, revised Jan. 1977
[16] Schaefer, H. H., Topological vector spaces, (1964) · Zbl 0212.14001
[17] Schaefer, HelmutH., Banach lattices and positive operators, (1974) · Zbl 0296.47023
[18] Titchmarsh, E. C., The Theory of Functions, (1939) · JFM 65.0302.01
[19] Varga, RichardS., Matrix iterative analysis, (1962) · Zbl 0133.08602
[20] Wielandt, Helmut, Unzerlegbare, nicht negative matrizen, Math. Z., 52, 642, (1950) · Zbl 0035.29101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.