## A test matrix for an inverse eigenvalue problem.(English)Zbl 1442.15012

Summary: We present a real symmetric tridiagonal matrix of order $$n$$ whose eigenvalues are $$\{2 k \}_{k = 0}^{n - 1}$$ which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, $$\{2 l + 1 \}_{l = 0}^{n - 2}$$. 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.

### MSC:

 15A18 Eigenvalues, singular values, and eigenvectors 15B57 Hermitian, skew-Hermitian, and related matrices
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### References:

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