Group inverse and group involutory Matrices∗

DOI10.1080/03081089808818587zbMath0949.15008OpenAlexW1980603302MaRDI QIDQ4942586

Rafael Bru, Nestor Janier Thome

Publication date: 21 March 2000

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081089808818587

zbMATH Keywords

Drazin inverseinteger matricesgeneralized inverseMoore-Penrose inversegroup inversegroup involutory matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Matrices of integers (15B36)

Related Items (17)

Symmetric singular linear control systems ⋮ Matrices \(A\) such that \(RA = A^{s+1}R\) when \(R^k = I\) ⋮ On a matrix group constructed from an \(\{ R,s+1,k \}\)-potent matrix ⋮ Relations between \(\{ K; s+1\} \)-potent matrices and different classes of complex matrices ⋮ Relationships between different sets involving group and Drazin projectors and nonnegativity ⋮ Oblique projectors and group involutory matrices ⋮ Generalized inverses and a block-rank equation. ⋮ The group involutory matrix of the combinations of two idempotent matrices ⋮ Characterizations of \(\{K,s+1\}\)-potent matrices and applications ⋮ On the spectrum of linear combinations of finitely many diagonalizable matrices that mutually commute ⋮ Spectral study of \(\{ R, s + 1, k \}\)- and \(\{R, s + 1, k, \ast \}\)-potent matrices ⋮ A geometrical approach on generalized inverses by Neumann-type series ⋮ Unnamed Item ⋮ Matrices whose powers approximate the identity ⋮ Special elements in a ring related to Drazin inverses ⋮ When is a linear combination of two idempotent matrices the group involutory matrix? ⋮ Characterizations of \(k\)-potent elements in rings.

Cites Work

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• A characterization of the Moore-Penrose inverse
• Neumann-type expansion of reflexive generalized inverses of a matrix and the hyperpower iterative method
• The group inverse of a triangular matrix
• On the group-inverse of a linear transformation
• About the group inverse and Moore-Penrose inverse of a product
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Generalized inverse of polynomial matrices
• Moore-penrose inverse of the incidence matrix of a tree
• A Characterization and Representation of the Drazin Inverse
• Singular values and maximum rank minors of generalized inverses
• Contributions to the Theory of Generalized Inverses

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