Positive symmetric matrices with exactly one positive eigenvalue

DOI10.1016/j.laa.2008.04.032zbMath1163.15024OpenAlexW2164373793MaRDI QIDQ1002259

Juan Manuel Peña

Publication date: 25 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.04.032

zbMATH Keywords

Gaussian eliminationpositive matricessymmetric matricesdoubly stochastic matrixconditionally negative definite matricesexactly one positive eigenvaluepivoting strategies

Mathematics Subject Classification ID

Factorization of matrices (15A23) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Direct numerical methods for linear systems and matrix inversion (65F05) Stochastic matrices (15B51)

Related Items

Sufficient conditions for symmetric matrices to have exactly one positive eigenvalue, Some classes of nonsingular matrices with applications to localize the real eigenvalues of real matrices

Cites Work

• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Characterizations and stable tests for the Routh--Hurwitz conditions and for total positivity
• A stable test for strict sign regularity
• A stable test to check if a matrix is a nonsingular $M$-matrix
• Exclusion and Inclusion Intervals for the Real Eigenvalues of Positive Matrices
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