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

Tatiana Klimchuk; Vladimir V. Sergeichuk

Special Matrices (2014)

- Volume: 2, Issue: 1, page 180-186, electronic only
- ISSN: 2300-7451

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topTatiana Klimchuk, and Vladimir V. Sergeichuk. "Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C." Special Matrices 2.1 (2014): 180-186, electronic only. <http://eudml.org/doc/269173>.

@article{TatianaKlimchuk2014,

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.},

author = {Tatiana Klimchuk, Vladimir V. Sergeichuk},

journal = {Special Matrices},

keywords = {Quaternion matrices; Consimilarity; Matrix equations; quaternion matrices; consimilarity; matrix equations; canonical form},

language = {eng},

number = {1},

pages = {180-186, electronic only},

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

url = {http://eudml.org/doc/269173},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Tatiana Klimchuk

AU - Vladimir V. Sergeichuk

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

JO - Special Matrices

PY - 2014

VL - 2

IS - 1

SP - 180

EP - 186, electronic only

AB - 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.

LA - eng

KW - Quaternion matrices; Consimilarity; Matrix equations; quaternion matrices; consimilarity; matrix equations; canonical form

UR - http://eudml.org/doc/269173

ER -

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