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

    Cite this

    Britz, T. (2004). On free matrices. (1 ed.) København: Department of Mathematics, Technical University of Denmark. MAT-Report, No. 2004-15
    Britz, Thomas. / On free matrices. 1 ed. København : Department of Mathematics, Technical University of Denmark, 2004. (MAT-Report; No. 2004-15).
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    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.",
    author = "Thomas Britz",
    year = "2004",
    language = "English",
    publisher = "Department of Mathematics, Technical University of Denmark",
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    Britz, T 2004, On free matrices. MAT-Report, no. 2004-15, 1 edn, Department of Mathematics, Technical University of Denmark, København.

    On free matrices. / Britz, Thomas.

    1 ed. København : Department of Mathematics, Technical University of Denmark, 2004. (MAT-Report; No. 2004-15).

    Research output: Book/ReportReportResearch

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    AB - 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.

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    Britz T. On free matrices. 1 ed. København: Department of Mathematics, Technical University of Denmark, 2004. (MAT-Report; No. 2004-15).