Liao, Jun; Liu, Heguo; Shao, Minfeng; Xu, Xingzhong A matrix identity and its applications. (English) Zbl 1310.15023 Linear Algebra Appl. 471, 346-352 (2015). Summary: We first prove a matrix identity concerning the blocks of generalized Jordan blocks and then give applications to some invariants of matrices. As a consequence, we reprove the well known fact that for an eigenvalue \(\lambda\), its algebraic multiplicity is greater than or equal to its geometric multiplicity. Cited in 1 Document MSC: 15A24 Matrix equations and identities 15A21 Canonical forms, reductions, classification 15A18 Eigenvalues, singular values, and eigenvectors Keywords:characteristic polynomial; minimal polynomial; rational canonical form; matrix identity; eigenvalue; algebraic multiplicity; geometric multiplicity PDFBibTeX XMLCite \textit{J. Liao} et al., Linear Algebra Appl. 471, 346--352 (2015; Zbl 1310.15023) Full Text: DOI References: [1] Bhattacharya, P. B.; Jain, S. K.; Nagpaul, S. R., Basic Abstract Algebra (1994), Cambridge University Press · Zbl 0837.00002 [2] Horn, R. A.; Johnson, C. R., Matrix Analysis (1990), Cambridge University Press · Zbl 0704.15002 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.