Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602502 | Linear Algebra and its Applications | 2009 | 14 Pages |
Abstract
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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