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

Abstract

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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.

How to cite

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Tatiana 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 -

References

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