Generalized Pascal matrices generate classes closed under multiplication

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    Abstract

    Classes of matrices which are the Hadamard product of a fixed lower triangular generating matrix P and any Toeplitz matrix are studied. These classes are generalizations of the special case when a Toeplitz matrix is generated by the vector of powers and P is either also Toeplitz or a Pascal triangle. The matrix P which lead to the class being closed under matrix multiplication is fully characterized. Explicit formulae for inverses are derived and commutativity of products within each class proven. Examples using lower triangular matrices with binomial coefficients are given.

    Original languageEnglish
    Pages (from-to)2887-2895
    Number of pages9
    JournalLinear Algebra and its Applications
    Volume437
    Issue number12
    DOIs
    Publication statusPublished - 15 Dec 2012

    Keywords

    • Classes of commuting matrices
    • Pascal matrices
    • Toeplitz matrices

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