An algebraic technique for total least squares problem in quaternionic quantum theory

The total least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector b=bm×1b=bm×1 and the data matrix A=Am×nA=Am×n. In this paper, we study the quaternion total least squares (QTLS) problem by means of real representations of quaternion matrices, and derive an algebraic technique for finding solutions of the QTLS problem in quaternionic quantum theory.