Determinantal representations of the Moore-Penrose inverse over the quaternion skew field and corresponding Cramer's rules

Mathematics – Rings and Algebras

Scientific paper

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26 pages, Forthcoming in Linear and Multilinear Algebra

Scientific paper

Determinantal representation of the Moore-Penrose inverse over the quaternion
skew field is obtained within the framework of a theory of the column and row
determinants. Using the obtained analogs of the adjoint matrix, we get the
Cramer rules for the least squares solution of left and right systems of
quaternionic linear equations.

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