A Test Matrix for an Inverse Eigenvalue Problem

We present a real symmetric tri-diagonal matrix of order n whose eigenvalues are \2k \ₖ₌₀ⁿ⁻¹ which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, \2l + 1 \ₗ₌₀ⁿ⁻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.