The completion problem for \(M\)-matrices and inverse \(M\)-matrices

DOI10.1016/0024-3795(95)00429-7zbMath0979.15009OpenAlexW2009770858MaRDI QIDQ1923169

Ronald L. Smith, Charles R. Johnson

Publication date: 25 November 1996

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00429-7

zbMATH Keywords

inverse problemmatrix completioninverse \(M\)-matrix\(M\)-matricespartial matrixdeterminant maximizing completionpositive definite completion

Mathematics Subject Classification ID

Inverse problems in linear algebra (15A29) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items

Matrix completions for linear matrix equations ⋮ Inverse \(M\)-matrix completion problem with zeros in the inverse completion ⋮ Note on subdirect sums of SDD(p) matrices ⋮ Note on subdirect sums of \(\{i_0\}\)-Nekrasov matrices ⋮ Path product matrices ⋮ On the solvability of derived matrix problems, including completions and duals ⋮ Completions of \(M\)-matrix patterns ⋮ Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures ⋮ Matrix completion problems for pairs of related classes of matrices. ⋮ Inverse M-matrices completions of then-chordal graph ⋮ Completions of P-matrix patterns ⋮ The symmetric \(M\)-matrix and symmetric inverse \(M\)-matrix completion problems ⋮ Graph theoretic methods for matrix completion problems ⋮ Inverse \(M\)-matrices. II ⋮ The doubly negative matrix completion problem ⋮ On \(\{P_1,P_2\}\)-Nekrasov matrices ⋮ Completions of inverse \(M\)-matrix patterns ⋮ Inverse \(M\)-matrix, a new characterization ⋮ Maximum likelihood estimation in Gaussian models under total positivity ⋮ \(P\)-matrix completions under weak symmetry assumptions ⋮ On OBS matrices and OBS-B matrices ⋮ Inverse \(M\)-matrix completions of patterns omitting some diagonal positions ⋮ Sub-direct sums and positivity classes of matrices ⋮ The symmetric inverse \(M\)-matrix completion problem ⋮ Local inversion of matrices with sparse inverses

Cites Work

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• Positive definite completions of partial Hermitian matrices
• Inverse M-matrices
• The dissimilarity characteristic of Husimi trees
• Matrix Analysis
• Matrices with chordal inverse zero-patterns
• Matrix inequalities

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