The equation X⊤AX=B with B skew-symmetric: how much of a bilinear form is skew-symmetric?

DOI10.1080/03081087.2022.2093825zbMath1527.15010arXiv2203.07100OpenAlexW4287148160MaRDI QIDQ6115878

Fernando De Terán, Roberto Canogar, Alberto Borobia

Publication date: 10 August 2023

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

Full work available at URL: https://arxiv.org/abs/2203.07100

zbMATH Keywords

consistencybilinear formskew-symmetric matrixcongruencematrix equationtransposecanonical form for congruence

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21)

Related Items (1)

On the consistency of the matrix equation \(X^\top AX = B\) when \(B\) is symmetric: the case where \(\mathrm{CFC}(A)\) includes skew-symmetric blocks

Cites Work

• Unnamed Item
• Canonical forms for congruence of matrices and \(T\)-palindromic matrix pencils: a tribute to H. W. Turnbull and A. C. Aitken
• On the solvability of a certain class of quadratic matrix equations
• The solution of the equation \(XA+AX^T=0\) and its application to the theory of orbits
• Palindromic linearization and numerical solution of nonsymmetric algebraic \(T\)-Riccati equations
• On the consistency of the matrix equation \(X^\top A X=B\) when \(B\) is symmetric
• On the solution of the nonsymmetric T-Riccati equation
• Canonical forms for complex matrix congruence and \(^{*}\)-congruence
• Representation by quadratic forms in a finite field
• Representations by skew forms in a finite field
• Solving cubic matrix equations arising in conservative dynamics

This page was built for publication: The equation X^⊤AX=B with B skew-symmetric: how much of a bilinear form is skew-symmetric?