Algebraic algorithms for least squares problem in quaternionic quantum theory Original Research Article

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations image that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory.