Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse

Abstract

Weighted singular value decomposition (WSVD) and a representation of the weighted Moore–Penrose inverse of a quaternion matrix by WSVD have been derived. Using this representation, limit and determinantal representations of the weighted Moore–Penrose inverse of a quaternion matrix have been obtained within the framework of the theory of noncommutative column-row determinants. By using the obtained analogs of the adjoint matrix, we get the Cramer rules for the weighted Moore–Penrose solutions of left and right systems of quaternion linear equations.