A Test Matrix for an Inverse Eigenvalue Problem

Abstract

We present a real symmetric tri-diagonal matrix of order $n$ whose eigenvalues are $\{2k{\}}_{k=0}^{n-1}$ which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, $\{2l+1{\}}_{l=0}^{n-2}$. The matrix entries are explicit functions of the size $n$, and so the matrix can be used as a test matrix for eigenproblems, both forward and inverse. An explicit solution of a spring-mass inverse problem incorporating the test matrix is provided.

References in corpus (1)

• A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices