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.