Article,

Diagonal Elements and Eigenvalues of a Real Symmetric Matrix

, and .
Journal of Mathematical Analysis and Applications, 91 (2): 562 - 566 (1983)
DOI: 10.1016/0022-247X(83)90171-3

Abstract

A simple and constructive proof is given for the existence of a real symmetric matrix with prescribed diagonal elements and eigenvalues. Numerically implementable algorithms for constructing such a matrix are discussed.

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