A note on matrix inversion

DOI10.1016/0024-3795(84)90177-0zbMath0533.15002OpenAlexW2029723395MaRDI QIDQ789471

William H. Gustafson

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0024-3795(84)90177-0

zbMATH Keywords

Smith canonical formmatrix inversion, principal ideal domain

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Canonical forms, reductions, classification (15A21)

Related Items

A note on the nullity theorem ⋮ Left multiples and right divisors of integral matrices ⋮ Minimal rank completions of partial banded matrices ⋮ Inverses of generalized Hessenberg matrices ⋮ On the closed representation for the inverses of Hessenberg matrices ⋮ The nullity theorem for principal pivot transform ⋮ Efficient Ehrlich-Aberth iteration for finding intersections of interpolating polynomials and rational functions ⋮ Nullities of submatrices of the Moore-Penrose inverse ⋮ Almost principal minors of inverse \(M\)-matrices ⋮ Gustafson’s Isomorphism and the Zassenhaus Lemma via a Common Commutative Diagram ⋮ Outer inverses: Jacobi type identities and nullities of submatrices ⋮ Complementary Schur complements ⋮ Fast Hessenberg Reduction of Some Rank Structured Matrices

Cites Work

• The Smith form, the inversion rule for 2x2 matrices, and the uniqueness of the invariant factors for finitely generated modules
• Matrices and pairs of modules
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