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Extremal inverse eigenvalue problem for a special kind of matrices. (English) Zbl 1406.15018

Summary: We consider the following inverse eigenvalue problem: to construct a special kind of matrix (real symmetric doubly arrow matrix) from the minimal and maximal eigenvalues of all its leading principal submatrices. The necessary and sufficient condition for the solvability of the problem is derived. Our results are constructive and they generate algorithmic procedures to construct such matrices.

MSC:

15A29 Inverse problems in linear algebra
15A18 Eigenvalues, singular values, and eigenvectors
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