The matrix equation \(XA=A^ TX\) and an associated algorithm for solving the inertia and stability problems

DOI10.1016/0024-3795(87)90143-1zbMath0634.93025OpenAlexW2030438400MaRDI QIDQ1097212

Karabi Datta, Biswa Nath Datta

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90143-1

zbMATH Keywords

algorithmmatrix equationsinertiaHessenberg matrix

Mathematics Subject Classification ID

Related Items (12)

The explicit solution of the matrix equation \(AX-XB = C\) ⋮ The linear bi-spatial tensor equation \(\varphi_{ij}A^iXB^j=C\) ⋮ On the matrix equation \(XH = HX\) and the associated controllability problem ⋮ Parallel algorithms for certain matrix computations ⋮ An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure ⋮ Solving the Sylvester Equation AX-XB=C when $\sigma(A)\cap\sigma(B)\neq\emptyset$ ⋮ Stability and inertia ⋮ Large-scale complex eigenvalue problems ⋮ On eigenvalue and canonical form assignments ⋮ Parallel and large-scale matrix computations in control: Some ideas ⋮ Generalized Hankel matrices of Markov parameters and their applications to control problems ⋮ Linear and numerical linear algebra in control theory: Some research problems

Uses Software

• Algorithm 432

Cites Work

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• On the similarity transformation between a matrix and its transpose
• The matrix equation \(XA-BX=R\) and its applications
• Fast projection methods for minimal design problems in linear system theory
• Controllability, observability and the solution of AX-XB=C
• An algorithm for computing powers of a Hessenberg matrix and its applications
• Computing powers of arbitrary Hessenberg matrices
• On the effective computation of the inertia of a non-hermitian matrix
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• Remarks on the root-clustering of a polynomial in a certain region in the complex plane
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• A Note on the Bezoutian Matrix
• A general theory for matrix root-clustering in subregions of the complex plane

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