$2\times2$ block representations of the Moore-Penrose inverse and orthogonal projection matrices
Bernd Fritzsche, Conrad M\"adler
TL;DR
This paper introduces new block matrix representations for Moore-Penrose inverses of complex 2x2 matrices, utilizing orthogonal projection matrices to simplify computations and analysis.
Contribution
It provides novel block representations for Moore-Penrose inverses of 2x2 matrices based on orthogonal projections, advancing matrix analysis techniques.
Findings
New block formulas for Moore-Penrose inverses of 2x2 matrices
Simplified computation of inverses using orthogonal projections
Enhanced understanding of matrix inverse structures
Abstract
In this paper, new block representations of Moore-Penrose inverses for arbitrary complex block matrices are given. The approach is based on block representations of orthogonal projection matrices.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · graph theory and CDMA systems