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
Publication date2004
Place of publicationKøbenhavn
PublisherDepartment of Mathematics, Technical University of Denmark
Edition1
StatePublished
NameMAT-Report
Number2004-15
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