Eigenvalues of completions of submatrices

DOI10.1080/03081088908817928zbMath0706.15011OpenAlexW2025368771MaRDI QIDQ3487561

Israel Gohberg, F. van Schagen, Marinus A. Kaashoek

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1080/03081088908817928

zbMATH Keywords

invariant polynomialseigenvalue completion problemblocks of maximal length or maximal widthcompletions of submatrices

Mathematics Subject Classification ID

Canonical forms, reductions, classification (15A21)

Related Items (33)

Completion of quasi-regular matrix pencils ⋮ A new approach to square matrix completion problem ⋮ Completion of matrix pencils with a single rank restriction ⋮ Feedback invariants of pairs of matrices and restrictions ⋮ On the eigenvalues of matrices with prescribed upper triangular part ⋮ Unnamed Item ⋮ Cyclic dimensions, controllability subspaces and Gohberg-Kaashoek numbers ⋮ Possible block similarity classes of a matrix with a prescribed nonprincipal submatrix. II ⋮ Operator blocks and quadruples of subspaces: Classification and the eigenvalue completion problem ⋮ Combinatorics of polynomial chains ⋮ The number of nonconstant invariant polynomials of matrices with several prescribed blocks ⋮ Powers of defective matrices from diagonalizable dilations ⋮ Pencils with prescribed constant subpencils ⋮ Row or Column Completion of Polynomial Matrices of Given Degree ⋮ On the eigenvalues of matrices with given upper triangular part ⋮ Matrix pencils completion problems. II ⋮ The General Matrix Pencil Completion Problem: A Minimal Case ⋮ Unified theorems on completions of matrix pencils ⋮ High, low, and quantitative roads in linear algebra ⋮ Matrix pencils completion problems ⋮ Similarity invariants of completions of submatrices ⋮ Jordan forms of completions of partial upper triangular matrices ⋮ Feedback invariants of restrictions -- a polynomial approach ⋮ Feedback invariants of matrices with prescribed rows ⋮ Characteristic polynomials and controllability of partially prescribed matrices ⋮ On the eigenvalues of matrices with prescribed upper triangular part ⋮ Similarity class of a matrix with a prescribed submatrix ⋮ Matrix completion problems ⋮ On the number of invariant factors of partially prescribed matrices and control theory ⋮ Feedback invariants via output injection ⋮ Possible block similarity classes of a matrix with a prescribed nonprincipal submatrix ⋮ A completion problem over the field of real numbers ⋮ On the number of invariant polynomials of partially prescribed matrices

Cites Work

• Matrices with prescribed rows and invariant factors
• Similarity of operator blocks and canonical forms. I. General results, feedback equivalence and Kronecker indices
• Interlacing inequalities for invariant factors
• Imbedding conditions for \(\lambda\)-matrices
• Unnamed Item
• Unnamed Item

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