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

摘要

Determinantal representation of the Moore-Penrose inverse over the quaternionskew field is obtained within the framework of a theory of the column and rowdeterminants. Using the obtained analogs of the adjoint matrix, we get theCramer rules for the least squares solution of left and right systems ofquaternionic linear equations.