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arXiv · 1604.00243

Determinantal representations of the quaternion weighted Moore-Penrose inverse and corresponding Cramer's rule

Ivan Kyrchei
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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.

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Ivan Kyrchei. 2016-04-01. Determinantal representations of the quaternion weighted Moore-Penrose inverse and corresponding Cramer's rule. https://arxiv.org/abs/1604.00243

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