Compound matrices: Properties, numerical issues and analytical computations

DOI10.1007/s11075-008-9222-7zbMath1168.65023OpenAlexW2169878318MaRDI QIDQ1014362

Marilena Mitrouli, Christos D. Kravvaritis

Publication date: 27 April 2009

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-008-9222-7

zbMATH Keywords

numerical examplesHadamard matricesdeterminantscompound matricessingular value decompositionsmatrix factorizationsdiagonal matricesspecial matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of determinants (65F40) Canonical forms, reductions, classification (15A21) Exterior algebra, Grassmann algebras (15A75)

Cites Work

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• On the computation of the Smith normal form of compound matrices
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• Matrix Analysis
• Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices
• Decentralized determinantal assignment problem: fixed and almost fixed modes and zeros
• Nullspaces of matrices and their compounds
• Use of geometric algebra: compound matrices and the determinant of the sum of two matrices
• Bounds on Norms of Compound Matrices and on Products of Eigenvalues
• Computation of the GCD of polynomials using gaussian transformations and shifting
• Compound matrices and three celebrated theorems

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