In this paper, we give a simple sufficient condition for the eigenvalue-separation properties of real tridiagonal matrices T. This result is much more than the statement that the pertinent eigenvalues are distinct. Its derivation is based on recurrence formulae satisfied by the polynomials made up by the minors of the characteristic polynomial det(xE-T) that are proven to form a Sturm sequence. This is a new result, and it proves the simple spectrum property of a symmetric tridiagonal matrix studied in Grünbaum's paper. Two numerical examples underpin the theoretical findings. The style of the paper is expository in order to address a large readership.
Characteristic polynomial Distinct eigenvalues Eigenvalue-separation properties Minors of determinant Sturm sequence Tridiagonal matrix
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Primary Language | English |
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Subjects | Numerical and Computational Mathematics (Other) |
Journal Section | Articles |
Authors | |
Early Pub Date | October 20, 2023 |
Publication Date | December 15, 2023 |
Published in Issue | Year 2023 |