Abstract
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.
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Stuart, J.L. Nested matrices and inverse M-matrices. Czech Math J 65, 537–544 (2015). https://doi.org/10.1007/s10587-015-0192-3
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DOI: https://doi.org/10.1007/s10587-015-0192-3