Completion of partial matrices to contractions

DOI10.1016/0022-1236(86)90091-1zbMath0626.47015OpenAlexW1965792141MaRDI QIDQ580679

Leiba Rodman, Charles R. Johnson

Publication date: 1986

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(86)90091-1

zbMATH Keywords

bipartite graphpartial matrixchordal graphnest algebraspartial contractioncompletability of a contraction

Mathematics Subject Classification ID

Paths and cycles (05C38) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Canonical models for contractions and nonselfadjoint linear operators (47A45)

Related Items

Completion of operator partial matrices to square-zero contractions ⋮ Combinatorial matrix analysis: An overview ⋮ Positive semidefinite matrices with a given sparsity pattern ⋮ Rank-preserving extensions of band matrices ⋮ On the Hermitian structures of the solution to a pair of matrix equations ⋮ Bounds for eigenvalues and singular values of matrix completions ⋮ Contractive symmetric matrix completion problems related to graphs ⋮ Matrix completions and chordal graphs ⋮ Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method ⋮ Lifting positive elements in \(C^*\)-algebras ⋮ A Schur parametrization of non-negative Hermitian and contractive block matrices and the corresponding maximum entropy problems ⋮ High, low, and quantitative roads in linear algebra ⋮ Caratheodory interpolation kernels ⋮ Idempotent completions of operator partial matrices ⋮ Completion of operator partial matrices to projections ⋮ Complex symmetric completions of partial operator matrices ⋮ Several results on chordal bipartite graphs ⋮ Relaxation of metric constrained interpolation and a new lifting theorem ⋮ Completion of Hankel partial contractions of extremal type

Cites Work

• Positive definite completions of partial Hermitian matrices
• The maximum distance problem and band sequences
• Extensions of band matrices with band inverses
• Interpolation problems in nest algebras
• An extremal problem for extensions of a sesquilinear form
• On a quotient norm and the Sz.-Nagy-Foias lifting theorem
• Inertia possibilities for completions of partial hermitian matrices^*
• The distance to upper triangular operators
• Norm-Preserving Dilations and Their Applications to Optimal Error Bounds
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