Nested matrices and inverse M-matrices
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Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the LU- and QR-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse M-matrices with symmetric, irreducible, tridiagonal inverses.
Keywordsnested matrix tridiagonal matrix inverse M-matrix principal minor determinant QR-factorization
MSC 201015A15 15A09 15B0
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