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

• Autorzy: Tatiana Klimchuk , Vladimir V. Sergeichuk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Quaternion matrices; Consimilarity; Matrix equations

Kategorie tematyczne

• 15A21: Canonical forms, reductions, classification
• 15A24: Matrix equations and identities
• 15B33: Matrices over special rings (quaternions, finite fields, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-06-12

zaakceptowano

2014-10-08

online

2014-12-01

Twórcy

autor

Tatiana Klimchuk

• Kiev National Taras Shevchenko University, Kiev, Ukraine

autor

Vladimir V. Sergeichuk

• Institute of Mathematics, Tereshchenkivska 3, Kiev, Ukraine

Bibliografia

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Identyfikatory

DOI

10.2478/spma-2014-0018