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Real Representation Approach to Quaternion Matrix Equation Involving ϕ-Hermicity
2019
Mathematical Problems in Engineering
For a quaternion matrix A, we denote by Aϕ the matrix obtained by applying ϕ entrywise to the transposed matrix AT, where ϕ is a nonstandard involution of quaternions. A is said to be ϕ-Hermitian or ϕ-skew-Hermitian if A=Aϕ or A=−Aϕ, respectively. In this paper, we give a complete characterization of the nonstandard involutions ϕ of quaternions and their conjugacy properties; then we establish a new real representation of a quaternion matrix. Based on this, we derive some necessary and
doi:10.1155/2019/3258349
fatcat:ccejgyd3wjb6pefgmcoe4pxqv4