The group inverse of the transformation \(\mathcal{S}(X)=AX-XB\)

DOI10.1016/S0024-3795(96)00165-6zbMath0874.15004MaRDI QIDQ1355223

Georg Heinig

Publication date: 3 November 1997

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

zbMATH Keywords

linear transformationgroup inversematrix inversionHankel matricesLyapunov transformationSylvester transformation

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Linear transformations, semilinear transformations (15A04)

Related Items (6)

Rank equalities and inequalities for Kronecker products of matrices with applications. ⋮ Group inverse for block matrix with \(t\)-potent subblock ⋮ Group inverse for a class of \(2\times 2\) anti-triangular block matrices over skew fields ⋮ Group inverse for the block matrices with an invertible subblock ⋮ Group inverse for two classes of \(2\times 2\) block matrices over rings ⋮ Matrices with higher order displacement structure

Cites Work

• Algebraic methods for Toeplitz-like matrices and operators
• Hankel matrices generated by the Markov parameters of rational functions
• Linear matrix equations: The module theoretic approach
• Algebraic method for the study of some linear matrix equations
• Generalized Lyapunov equations, matrices with displacement structure, and generalized Bézoutians
• Matrix calculations for Liapunov quadratic forms
• $AX - XB = C$, Resultants and Generalized Inverses
• Formulae for the solution of Lyapunov matrix equations
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