四元数体上矩阵的弱直积与弱圈积

WEAK DIRECT PRODUCTS AND WEAK CIRCULAR PRODUCTS OF MATRICES OVER THE REAL QUATERNION DIVISION RING

This paper introduces the ideas of the so-called "Weak direct product" and "Weak circular product" of matrices over the real quarternion division ring, and gives not only some basic properties of these matrices, but also some new results on Xie's determinant for the weak direct product of the positive selfconjugate matric- es. Some generalized and new results involving the weak circular product of the positive selfconjugate matrices as well as of the so-called "weak positive definite selfconjugate matrices" are also given in this paper. Consequently, some famous theorems in the ordinary matrix theory are but their special cases.