publication . Article . 2005

On generalized quadratic matrices

Richard W. Farebrother; Götz Trenkler;
Open Access English
  • Published: 01 Nov 2005 Journal: Linear Algebra and its Applications (issn: 00243795, Copyright policy)
  • Publisher: Elsevier Inc.
Abstract In this paper a wide class of matrices is considered, containing idempotent, involutory, nilpotent and several other types of matrices. Extending an approach considered by Radjavi and Rosenthal [H. Radjavi, P. Rosenthal, On commutators of idempotents, Linear Multilinear Algebra 50 (2) (2002) 121–124], we investigate the set Q ( P ) of square matrices A ∈ C n × n satisfying the equation A 2  =  α A  +  β P for some complex numbers α and β and for some n  ×  n nonzero complex idempotent matrix P such the AP  =  PA  =  A . Special attention is paid to the Moore–Penrose and group inverse of matrices belonging to Q ( P ) .
free text keywords: Generalized quadratic matrices, Idempotent matrix, Eigenvalue, Moore–Penrose inverse, Group inverse, Geometry and Topology, Algebra and Number Theory, Numerical Analysis, Discrete Mathematics and Combinatorics, Idempotence, Mathematics, Nilpotent, Nilpotent group, Matrix (mathematics), Moore–Penrose pseudoinverse, Combinatorics, Eigenvalues and eigenvectors, Square matrix
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