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., Jeffrey L. Stuart., and Obsahuje seznam literatury
A matrix whose entries consist of elements from the set $\lbrace +,-,0\rbrace $ is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.