Block generalized inverses
Copyright policy )Block generalized inverses
The existence of the Moore-Penrose inverse is discussed for elements of a *-regular ring \(R\). A technique is developed for computing conditional and reflexive inverses for matrices in \(R_{2\times 2}\), which is then used to calculate the Moore-Penrose inverse for these matrices. Several applications are given, generalizing many of the classical results; in particular, we shall emphasize the cases of bordered matrices, Schur complements, block-rank formulae and EP elements.
- North Carolina State University United States
- North Carolina Agricultural and Technical State University United States
*-regular ring, Matrices over special rings (quaternions, finite fields, etc.), block-rank formulae, von Neumann regular rings and generalizations (associative algebraic aspects), Theory of matrix inversion and generalized inverses, Schur complements, computing conditional and reflexive inverses, Moore-Penrose inverse, bordered matrices, EP elements
*-regular ring, Matrices over special rings (quaternions, finite fields, etc.), block-rank formulae, von Neumann regular rings and generalizations (associative algebraic aspects), Theory of matrix inversion and generalized inverses, Schur complements, computing conditional and reflexive inverses, Moore-Penrose inverse, bordered matrices, EP elements
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