Similarity invariants of completions of submatrices

DOI10.1016/0024-3795(92)90176-BzbMath0764.15007MaRDI QIDQ1187390

Isabel Cabral, Fernando Conceição Silva

Publication date: 23 July 1992

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

zbMATH Keywords

matrix pencilsinvariant polynomialssimilarity invariantscompletion of a submatrix

Mathematics Subject Classification ID

Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Related Items (27)

Completion of quasi-regular matrix pencils ⋮ A new approach to square matrix completion problem ⋮ Completion of matrix pencils with a single rank restriction ⋮ On the eigenvalues of matrices with prescribed upper triangular part ⋮ Unnamed Item ⋮ Matrices with prescribed submatrices and number of invariant polynomials ⋮ Possible block similarity classes of a matrix with a prescribed nonprincipal submatrix. II ⋮ Minimal completion problem for quasi-regular matrix pencils ⋮ On feedback equivalence and completion problems ⋮ Combinatorics of polynomial chains ⋮ Special loop connections of linear systems ⋮ Pencils with prescribed constant subpencils ⋮ Row or Column Completion of Polynomial Matrices of Given Degree ⋮ Ranks of submatrices and the off-diagonal indices of a square matrix ⋮ Matrix pencils completion problems. II ⋮ The General Matrix Pencil Completion Problem: A Minimal Case ⋮ Matrix pencils completion problems ⋮ Products of two involutions with prescribed eigenvalues and some applications ⋮ Subrepresentations of Kronecker representations. ⋮ Invariant factor assignment under state feedback and output injection ⋮ Feedback invariants of a pair of matrices with prescribed columns ⋮ On the eigenvalues of matrices with prescribed upper triangular part ⋮ Similarity class of a matrix with a prescribed submatrix ⋮ On the number of invariant factors of partially prescribed matrices and control theory ⋮ Possible block similarity classes of a matrix with a prescribed nonprincipal submatrix ⋮ Assigning the Kronecker invariants of a matrix pencil by row or column completions ⋮ On the number of invariant polynomials of partially prescribed matrices

Cites Work

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• Interlacing inequalities and control theory
• Interlacing inequalities for regular pencils
• Matrices with prescribed characteristic polynomial and principal blocks. II
• Unified theorems on completions of matrix pencils
• Interlacing inequalities for invariant factors
• Imbedding conditions for \(\lambda\)-matrices
• Existenzsätze in der Theorie der Matrizen und lineare Kontrolltheorie
• Matrices with prescribed characteristic polynomial and a prescribed submatrix. III
• Matrices with prescribed invariant factors and off-diagonal submatrices
• Eigenvalues of completions of submatrices
• Matrices with prescribed characteristic polynomial and principal blocks
• Matrices with prescribed submatrices

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