Yahaghi, B., Najafi, E. (2018). A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices. Wavelet and Linear Algebra, 4(3 (Special issue)), 97-148. doi: 10.22072/wala.2018.85963.1170

Bamdad Yahaghi; Elahe Najafi. "A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices". Wavelet and Linear Algebra, 4, 3 (Special issue), 2018, 97-148. doi: 10.22072/wala.2018.85963.1170

Yahaghi, B., Najafi, E. (2018). 'A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices', Wavelet and Linear Algebra, 4(3 (Special issue)), pp. 97-148. doi: 10.22072/wala.2018.85963.1170

Yahaghi, B., Najafi, E. A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices. Wavelet and Linear Algebra, 2018; 4(3 (Special issue)): 97-148. doi: 10.22072/wala.2018.85963.1170

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

^{2}Department of Mathematics, Golestan University

Abstract

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More precisely, we prove that every bounded group of matrices with quaternion entries is similar to a group of unitary quaternion matrices.

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