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Strict diagonal dominance and a Geršgorin type theorem in Euclidean Jordan algebras

✍ Scribed by Melania M. Moldovan; M. Seetharama Gowda

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 194 KB
Volume: 431
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.02.016

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✦ Synopsis

For complex square matrices, the Levy-Desplanques theorem asserts that a strictly diagonally dominant matrix is invertible. The well-known Geršgorin theorem on the location of eigenvalues is equivalent to this. In this article, we extend the Levy-Desplanques theorem to an object in a Euclidean Jordan algebra when its Peirce decomposition with respect to a Jordan frame is given. As a consequence, we prove a Geršgorin type theorem for the spectral eigenvalues of an object in a Euclidean Jordan algebra.

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