On solutions of the matrix equation T'AT=A\(^2\)

DOI10.1016/0024-3795(74)90080-9zbMath0288.15019OpenAlexW2077908460MaRDI QIDQ1846473

P. J. Bushell

Publication date: 1974

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

Full work available at URL: https://doi.org/10.1016/0024-3795(74)90080-9

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (10)

The Cayley-Hilbert metric and positive operators ⋮ The positive definite solution of the nonlinear matrix equation \(X^p = A + M(B + X^{-1})^{-1} M^\ast\) ⋮ Nonlinear equations based on jointly homogeneous mappings ⋮ Hilbert's metric and positive contraction mappings in a Banach space ⋮ Application of Hilbert's projective metric on symmetric cones ⋮ Solving an operator equation by iteration ⋮ On the solution of the nonlinear matrix equation \(X^n=f(X)\) ⋮ A new inversion-free iterative method for solving a class of nonlinear matrix equations ⋮ Unnamed Item ⋮ Applications of Hilbert's projective metric to a class of positive nonlinear operators

Cites Work

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• Hilbert's metric and positive contraction mappings in a Banach space
• An elementary proof of the Hopf inequality for positive operators
• Extensions of Jentzsch's Theorem
• On the Projective Contraction Ratio for Positive Linear Mappings

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