We present a real symmetric tridiagonal matrix of order whose eigenvalues are which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, . The matrix entries are explicit functions of the size , 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.
"A Test Matrix for an Inverse Eigenvalue Problem." J. Appl. Math. 2014 (SI04) 1 - 6, 2014. https://doi.org/10.1155/2014/515082