Cramer's rule for the general solution to a restricted system of quaternion matrix equations
type: Item
instance of: scholarly article
title: Cramer's rule for the general solution to a restricted system of quaternion matrix equations
zbMATH Open document ID: 1439.15006
author: G. J. Song
author: Shao-Wen Yu
published in: Advances in Applied Clifford Algebras
publication date: 2019-11-27T00:00:00Z
review text: Let \(\mathbb{H}^{m \times n}\) denote the set of all \(m \times n\) matrices over the quaternion algebra \[ \mathbb{H} = \{a_0 + a_1 i + a_2 j + a_3 k: i^2 = j^2 = k^2 = ijk = -1,\, a_0, a_1, a_2, a_3 \in \mathbb{R}\}. \] The authors study the following restricted system of quaternion matrix equations \[ A_1 X B_1 = C_1, \; A_2 X B_2 = C_2, \] under the assumptions \(\mathcal{R}_r(X) \subset T\) and \(\mathcal{N}_r(X) \supset S\), and the restricted generalized quaternion Sylvester equation \[ AXB + CYD = E, \] under the assumptions \(\mathcal{R}_r(X) \subset T_1\), \(\mathcal{N}_r(X) \supset S_1\), \(\mathcal{R}_r(Y) \subset T_2\) and \(\mathcal{N}_r(Y) \supset S_2\). Here, \(\mathcal{R}_r(A)\) and \(\mathcal{N}_r(A)\) denote the right range space and the right null space of \(A \in \mathbb{H}^{m \times n}\), respectively. The authors provide a number of Cramer rules for the general solutions to the above systems of matrix equations.
reviewed by: Jaydeb Sarkar
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 7137686
zbMATH Keywords: quaternion matrix
zbMATH Keywords: Cramer rule
zbMATH Keywords: matrix equations
zbMATH Keywords: determinant
MaRDI profile type: Publication
full work available at URL: s00006-019-1000-1
OpenAlex ID: W2973751704
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DOI: 10.1007/S00006-019-1000-1
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description: scientific article; zbMATH DE number 7137686