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Special Matrices

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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C

Tatiana Klimchuk / Vladimir V. Sergeichuk
Published Online: 2014-12-01 | DOI: https://doi.org/10.2478/spma-2014-0018

Abstract

L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331 (2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformations A ↦ ˜S−1AS in which S is a nonsingular quaternion matrix and h = a + bi + cj + dk ↦ ˜h := a − bi + cj − dk (a, b, c, d ∈ ℝ). We give an analogous canonical form of a quaternion matrix with respect to consimilarity transformations A ↦^S−1AS in which h ↦ ^h is an arbitrary involutive automorphism of the skew field of quaternions. We apply the obtained canonical form to the quaternion matrix equations AX −^X B = C and X − A^X B = C.

Keywords: Quaternion matrices; Consimilarity; Matrix equations

MSC: 15A21; 15A24; 15B33

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About the article

Received: 2014-06-12

Accepted: 2014-10-08

Published Online: 2014-12-01


Citation Information: Special Matrices, Volume 2, Issue 1, ISSN (Online) 2300-7451, DOI: https://doi.org/10.2478/spma-2014-0018.

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© 2014 Tatiana Klimchuk, Vladimir V. Sergeichuk. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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