Invertible Selfadjoint Extensions of Band Matrices and Their Entropy

DOI10.1137/0608040zbMath0634.47005OpenAlexW2066910060MaRDI QIDQ3772757

Israel Gohberg, David C. Lay, Robert L. Ellis

Publication date: 1987

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0608040

zbMATH Keywords

Toeplitz matrixmaximum entropy principleband extensionm-band matrixunique positive definite extension

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators (47A68) Dilations, extensions, compressions of linear operators (47A20)

Related Items

Hermitian completions of band matrices and applications ⋮ On two theorems of M. G. Krein concerning polynomials orthogonal on the unit circle ⋮ Invertible completions of band matrices ⋮ Nonstationary Szegö theorem, band sequences and maximum entropy ⋮ Positive semidefinite matrices with a given sparsity pattern ⋮ Rank-preserving extensions of band matrices ⋮ Bordered matrices ⋮ On negative eigenvalues of selfadjoint eztensions of band matrices ⋮ Positive semidefinite completions of partial Hermitian matrices ⋮ Orthogonal systems related to infinite Hankel matrices

Cites Work

• Positive definite completions of partial Hermitian matrices
• Determinantal formulae for matrices with sparse inverses
• Extensions of band matrices with band inverses
• Inverses of banded matrices
• The possible inertias for a Hermitian matrix and its principal submatrices
• Inertia possibilities for completions of partial hermitian matrices^*
• Unnamed Item