The Moore-Penrose inverse over a commutative ring

DOI10.1016/0024-3795(92)90318-5zbMath0764.15002OpenAlexW2055208051WikidataQ127763884 ScholiaQ127763884MaRDI QIDQ1208263

Donald W. Robinson, Ravindra B. Bapat

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1016/0024-3795(92)90318-5

zbMATH Keywords

Moore-Penrose inverseinvolutioncommutative ringdeterminantal rankMoore idempotentMoore invertible matrices

Mathematics Subject Classification ID

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

Related Items

The Moore idempotents of a matrix ⋮ Generalized inverses of matrices over commutative rings ⋮ The determinal rank idempotents of a matrix ⋮ Outer inverses and Jacobi type identities ⋮ Miscellaneous reverse order laws for generalized inverses of matrix products with applications ⋮ Moore-Penrose Dagger Categories ⋮ On matrices over an arbitrary semiring and their generalized inverses ⋮ Computation of all generalized inverses of an intuitionistic fuzzy matrix1 ⋮ The generalized inverse over commutative rings ⋮ The classical adjoint ⋮ Outer inverses of matrices ⋮ Group inverses and Drazin inverses over Banach algebras ⋮ Outer inverses: Jacobi type identities and nullities of submatrices

Cites Work

• Symmetric morphisms and the existence of Moore-Penrose inverses
• Generalized inverses over integral domains
• Categories of matrices with only obvious Moore-Penrose inverses
• Group and Moore-Penrose inverses of regular morphisms with kernel and cokernel
• The Moore-Penrose inverse of a morphism with factorization
• Integral generalized inverses of integral matrices
• Three results in connection with inverse matrices
• Das verallgemeinerte Inverse einer Matrix, deren Elemente einem beliebigen Körper angehören.
• Das verallgemeinerte Inverse einer Matrix über einem beliebigen Körper - analytisch betrachtet.
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