On the generalized nullspace of M-matrices and Z-matrices

DOI10.1016/0024-3795(88)90019-5zbMath0647.15005OpenAlexW2137665908MaRDI QIDQ1104377

Hans Schneider, Daniel Hershkowitz

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90019-5

zbMATH Keywords

M-matrixFrobenius normal formZ-matrixreduced graphpreferred basis

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Canonical forms, reductions, classification (15A21)

Related Items (17)

Combinatorial bases, derived jordan sets and the equality of the height and level characteristics of anM-matrix ⋮ Asymptotic exponential cones of Metzler matrices and their use in the solution of an algebraic problem ⋮ On the zero pattern properties and asymptotic behavior of continuous-time positive system trajectories ⋮ Solutions of Z-matrix equations ⋮ Characterizations and classifications of M-matrices using generalized nullspaces ⋮ The combinatorial structure of the generalized nullspace of a block triangular matrix ⋮ Positive root vectors ⋮ On the distinguished eigenvalues of a cone-preserving map ⋮ The combinatorial structure of generalized eigenspaces -- from nonnegative matrices to general matrices ⋮ On the existence of matrices with prescribed height and level characteristics ⋮ The Perron generalized eigenspace and the spectral cone of a cone-preserving map ⋮ Peak characteristic and nonnegative signature ⋮ Height bases, level bases, and the equality of the height and the level characteristics of anM-matrix ⋮ On the Perron roots of principal submatrices of co-order one of irreducible nonnegative matrices ⋮ On the invariant faces associated with a cone-preserving map ⋮ Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings ⋮ Linear equations over cones and Collatz-Wielandt numbers

Cites Work

• The influence of the marked reduced graph of a nonnegative matrix on the Jordan form and on related properties: a survey
• Solutions of Z-matrix equations
• Characterizations and classifications of M-matrices using generalized nullspaces
• Algebraic eigenspaces of nonnegative matrices
• On the singular graph and the Weyl characteristic of an M-matrix
• On Nonnegative Solutions of Matrix Equations
• Unnamed Item

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