A real quaternion matrix equation with applications

Solution to a system of real quaternion matrix equations encompassing η-Hermicity

“…The outcome of our exposition extends the noteworthy result of [28,32,33] and [46]. Furthermore, we have given an algorithm and a numerical example to interpret our rudimentary consequence.…”

Theη-bihermitian solution to a system of real quaternion matrix equations

“…Recently, Horn and Zhang [2] provided an analogous special singular value decomposition for η-Hermitian matrices. Yuan and Wang [44] derived the expressions of the least squares η-Hermitian solution of the real quaternion matrix equation AX B + C X D = E. Very recently, He and Wang [18] considered a real quaternion matrix equation involving η-Hermicity, i.e.…”

“…He and Wang [18] provided some necessary and sufficient conditions for the existence of a solution (X, Y, Z ) to the equation and presented a general solution when the equation is solvable. They also investigated some properties of the quaternion matrix A η * in [18].…”

“…They proposed the factorization of an η-Hermitian matrix A, and considered some properties of quaternion matrix involutions. Recently, He and Wang [18] studied some properties of Moore-Penrose inverse concerning quaternion matrix involutions. A group of formulas for quaternion matrix involutions given in the following Lemma.…”

“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]). In mathematics, engineering, and others, many problems can be transformed into some linear matrix equations.…”