Determinantal representations of the quaternion weighted Moore-Penrose inverse and corresponding Cramer's rule
arXiv:1604.00243
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 the 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.
arXiv commentarXiv admin note: text overlap with arXiv:1005.0736, arXiv:1503.03668, arXiv:1307.4281