On free matrices

Publication: ResearchReport – Annual report year: 2004

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Bipartite graphs and digraphs are used to describe algebraic operations on a free matrix, including Moore-Penrose inversion, finding Schur complements, and normalized LU factorization. A description of the structural properties of a free matrix and its Moore-Penrose inverse is proved, and necessary and sufficient conditions are given for the Moore-Penrose inverse of a free matrix to be free. Several of these results are generalized with respect to a family of matrices that contains both the free matrices and the nearly reducible matrices.
Original languageEnglish
Place of publicationKøbenhavn
PublisherDepartment of Mathematics, Technical University of Denmark
Edition1
StatePublished - 2004
NameMAT-Report
Number2004-15
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