On free matrices

Thomas Britz

    Research output: Book/ReportReportResearch

    Abstract

    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
    Publication statusPublished - 2004
    SeriesMAT-Report
    Number2004-15

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