Author： He Zhuo-Heng Wang Qing-Wen
Publisher： Taylor & Francis Ltd
ISSN： 0308-1087
Source： Linear and Multilinear Algebra, Vol.61, Iss.6, 2013-06, pp. : 725-740
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Abstract
Let i, j, k be the quaternion units and let A be a square real quaternion matrix. A is said to be η-Hermitian if −η A*η = A, where η ∈ {i, j, k} and A* is the conjugate transpose of A. Denote A η* = − η A*η. Following Horn and Zhang's recent research on η-Hermitian matrices (A generalization of the complex AutonneTakagi factorization to quaternion matrices, Linear Multilinear Algebra, DOI:10.1080/03081087.2011.618838), we consider a real quaternion matrix equation involving η-Hermicity, i.e.
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