A system of real quaternion matrix equations with applications

• Published in: Linear algebra and its applications Vol. 431; no. 12; pp. 2291 - 2303
• Main Authors: Wang, Qing-Wen, van der Woude, J.W., Chang, Hai-Xia
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.12.2009; Elsevier
• Subjects: [formula omitted]-symmetric matrix; Algebra; Exact sciences and technology; Inner inverse of a matrix; Linear and multilinear algebra, matrix theory; Mathematics; Moore–Penrose inverse of a matrix; Quaternion matrix; Reflexive inverse of a matrix; Sciences and techniques of general use; System of matrix equations; Quaternion matrix; Moore–Penrose inverse of a matrix; 15A24; 15A57; 15A33; 15A06; Reflexive inverse of a matrix; Inner inverse of a matrix; 15A09; System of matrix equations; ( P , Q ) -symmetric matrix; Existence of solution; Moore Penrose inverse; Quaternion; Moore-Penrose inverse of a matrix; Generalized inverse; Commutativity; Algebra; Inverse matrix; Matrix equation; Real matrix; Operator equation; (P, Q)-symmetric matrix; Involution; Linear system; Matrix inversion; Symmetric matrix; Ring; Solvability

Let H be the real quaternion algebra and H n × m denote the set of all n × m matrices over H . Let P ∈ H n × n and Q ∈ H m × m be involutions, i.e., P 2 = I , Q 2 = I . A matrix A ∈ H n × m is said to be ( P , Q ) -symmetric if A = PAQ . This paper studies the system of linear real quaternion matrix...