On the eigenvalues of matrices with given upper triangular part

DOI10.1007/BF01210399zbMath0706.15010OpenAlexW2022536501MaRDI QIDQ919062

Leiba Rodman, Tamir Shalom, Israel Gohberg, Joseph A. Ball

Publication date: 1990

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01210399

zbMATH Keywords

prescribed eigenvaluesmatrix completionfixed upper triangular matrixminimal spectral radius

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (21)

On the eigenvalues of matrices with prescribed upper triangular part ⋮ Nilpotent completions of partial upper triangular matrices ⋮ Completions of partial Jordan and Hessenberg matrices ⋮ Geometric multiplicities of completions of partial triangular matrices ⋮ On the solvability of polynomial systems arising in control ⋮ On a conjecture about the Jordan form of completions of partial upper triangular matrices ⋮ Jordan structures of upper equivalent matrices ⋮ Jordan structures of strictly lower triangular completions of nilpotent matrices ⋮ Eigenvalues of matrices with given block upper triangular part ⋮ Special loop connections of linear systems ⋮ On controllability of partially prescribed matrices ⋮ A classification of upper equivalent matrices. The generic case ⋮ Normal forms of generic triangular band matrices and Jordan forms of nilpotent completions ⋮ Matrix extensions and eigenvalue completions, the generic case ⋮ Jordan forms of completions of partial upper triangular matrices ⋮ On the Jordan form of completions of partial upper triangular matrices ⋮ Controllability and completion of partial upper triangular matrices over rings ⋮ On the eigenvalues of matrices with prescribed upper triangular part ⋮ Controllability by completions of partial upper triangular matrices ⋮ Completion of operator partial matrices to projections ⋮ On the number of invariant polynomials of partially prescribed matrices

Cites Work

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• Matrices with prescribed rows and invariant factors
• Matrices with prescribed eigenvalues and principal submatrices
• Matrices with prescribed characteristic polynomial and principal blocks. II
• Interlacing inequalities for invariant factors
• Imbedding conditions for \(\lambda\)-matrices
• Matrices with Prescribed Characteristic Roots and Diagonal Elements
• Matrices with prescribed invariant factors and off-diagonal submatrices
• Eigenvalues of completions of submatrices
• Mathematical Aspects of the Relative Gain Array $( A \circ A^{ - T} )$

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