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.
@article{bwmeta1.element.doi-10_2478_spma-2014-0018,
author = {Tatiana Klimchuk and Vladimir V. Sergeichuk},
title = {Consimilarity and quaternion matrix equations AX -^X B = C, X - A^X B = C},
journal = {Special Matrices},
volume = {2},
year = {2014},
zbl = {1310.15022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0018}
}
Tatiana Klimchuk; Vladimir V. Sergeichuk. Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0018/
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