Geodesic
Nested matrices and inverse $M$-matrices
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 537-544

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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.
DOI : 10.1007/s10587-015-0192-3
Classification : 15A09, 15A15, 15B05
Keywords: nested matrix; tridiagonal matrix; inverse $M$-matrix; principal minor; determinant; $QR$-factorization 
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Stuart, Jeffrey L. Nested matrices and inverse $M$-matrices. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 537-544. doi: 10.1007/s10587-015-0192-3

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