This paper gives differently a necessary and sufficient condition of existence of the solutions and Cramer formulas of linear equations, the related property of vector, opposite and rank of matrix, and characteristic root and characteristic vector of linear transformation etc by setting up a weakly exchangaeble law of quaternion product, and obtain a effective solution of the problems.
Shi Jin WU.
Obvious Formulas of a Certain Number Linear Algebra Problems over Quaternion Field. Acta Mathematica Sinica, Chinese Series, 2001, 44(5): 837-842 https://doi.org/10.12386/A2001sxxb0107