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

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 transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix and h = a + bi + cj + dk ↦ ˜h := a − bi + cj −...

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Main Authors:	Klimchuk Tatiana, Sergeichuk Vladimir V.
Format:	Article
Language:	English
Published:	De Gruyter 2014-02-01
Series:	Special Matrices
Subjects:	quaternion matrices consimilarity matrix equations 15a21 15a24 15b33
Online Access:	https://doi.org/10.2478/spma-2014-0018

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spelling	doaj-d97ff655733145b091382aecbba848f62021-10-02T19:16:02ZengDe GruyterSpecial Matrices2300-74512014-02-012110.2478/spma-2014-0018spma-2014-0018Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = CKlimchuk Tatiana0Sergeichuk Vladimir V.1Kiev National Taras Shevchenko University, Kiev, UkraineInstitute of Mathematics, Tereshchenkivska 3, Kiev, UkraineL. 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 transformationsA ↦ ˜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 transformationsA ↦^S−1AS in which h ↦ ^h is an arbitrary involutive automorphism of the skew field of quaternions. Weapply the obtained canonical form to the quaternion matrix equations AX −^X B = C and X − A^X B = C.https://doi.org/10.2478/spma-2014-0018quaternion matricesconsimilaritymatrix equations15a21 15a24 15b33
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Klimchuk Tatiana Sergeichuk Vladimir V.
spellingShingle	Klimchuk Tatiana Sergeichuk Vladimir V. Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C Special Matrices quaternion matrices consimilarity matrix equations 15a21 15a24 15b33
author_facet	Klimchuk Tatiana Sergeichuk Vladimir V.
author_sort	Klimchuk Tatiana
title	Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
title_short	Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
title_full	Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
title_fullStr	Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
title_full_unstemmed	Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
title_sort	consimilarity and quaternion matrix equations ax −^x b = c, x − a^x b = c
publisher	De Gruyter
series	Special Matrices
issn	2300-7451
publishDate	2014-02-01
description	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 transformationsA ↦ ˜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 transformationsA ↦^S−1AS in which h ↦ ^h is an arbitrary involutive automorphism of the skew field of quaternions. Weapply the obtained canonical form to the quaternion matrix equations AX −^X B = C and X − A^X B = C.
topic	quaternion matrices consimilarity matrix equations 15a21 15a24 15b33
url	https://doi.org/10.2478/spma-2014-0018
work_keys_str_mv	AT klimchuktatiana consimilarityandquaternionmatrixequationsaxxbcxaxbc AT sergeichukvladimirv consimilarityandquaternionmatrixequationsaxxbcxaxbc
_version_	1716847544373346304

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

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