Mapping and preserver properties of the principal pivot transform

DOI10.1080/03081080600821597zbMath1152.15003OpenAlexW2012103532MaRDI QIDQ3502316

Olga Slyusareva, Michael J. Tsatsomeros

Publication date: 23 May 2008

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

Full work available at URL: https://doi.org/10.1080/03081080600821597

zbMATH Keywords

Schur complementprincipal pivot transform\(P\)-matrixHermitian part\(N\)-matrixLeft eigenspace

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Algorithmic detection and construction of N-matrices, Generalized principal pivot transform, On hidden \(\mathbf{Z}\)-matrices and the linear complementarity problem, The almost semimonotone matrices, Semimonotone matrices

Cites Work

• Principal minors. I: A method for computing all the principal minors of a matrix
• Schur complements and statistics
• A generalization of N-matrices
• Almost skew-symmetric matrices
• Principal pivot transforms: Properties and applications
• Almost N-matrices and linear complementarity
• Some Aspects of the Theory of $PN$-Matrices