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arXiv · 1502.08014

Localization theorems for matrices and bounds for the zeros of polynomials over a quaternion division algebra

Sk. Safique Ahmad·Istkhar Ali
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Abstract

In this paper, Ostrowski and Brauer type theorems are derived for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic matrix. Thereafter a sufficient condition for the stability of a quaternionic matrix is given that generalizes the stability condition for a complex matrix. Finally, a characterization of bounds for the zeros of quaternionic polynomials is presented.

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Sk. Safique Ahmad, Istkhar Ali. 2015-01-17. Localization theorems for matrices and bounds for the zeros of polynomials over a quaternion division algebra. https://arxiv.org/abs/1502.08014

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