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

DOI10.1007/s13398-023-01391-0OpenAlexW4318336366MaRDI QIDQ2681738

Fernando De Terán, Alberto Borobia, Roberto Canogar

Publication date: 6 February 2023

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.02312

zbMATH Keywords

Riccati equationsymmetric matrixbilinear formcongruencematrix 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)

Cites Work

• 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
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• Palindromic linearization and numerical solution of nonsymmetric algebraic \(T\)-Riccati equations
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• On the solution of the nonsymmetric T-Riccati equation
• Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms
• Canonical forms for complex matrix congruence and \(^{*}\)-congruence
• A skew matrix equation over a finite field
• Representations by skew forms in a finite field
• Solving cubic matrix equations arising in conservative dynamics
• The Number of Solutions to the Matrix Equation XAX ^T = C, A and C Nonalternate and of Full Rank, Over GF (2^y )
• Rank r Solutions to the Matrix Equation XAX T = C, A Alternate, Over GF(2 y )
• Rank r Solutions to the Matrix Equation XAX^T = C, A Nonalternate, C Alternate, Over GF(2^y).
• The number of solutions to the alternate matrix equation over a finite field and a \(q\)-identity
• The equation X^⊤AX=B with B skew-symmetric: how much of a bilinear form is skew-symmetric?

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