有限维中心代数上矩阵方程组的广对称解与斜广对称解

Persymmetric and Perskewsymmetric Solutions to Sets of Matrix Equations over a Finite Central Algebra

设Ω是一个具有对合反自同构的有限维中心代数且charΩ≠2.本文在Ω上定义了广对称矩阵和斜广对称矩阵,在Ω[λ]上考虑了三个矩阵方程组,分别给出了其有广对称解和斜广对称的充要条件.作为特例,得到了某些矩阵方程相应的结果.

Let Ω be a finite dimensional central algebra with an involutorial antiauto-morphism and char Ω≠2. Persymmetric and perskewsymmetric matrices over Ω are defined. Three systems of matrix equations over Ω[λ] are considered. Necessary and sufficient conditions for the existences of constant solutions with persymmmetric and perskewsymmetric constraints to the systems mentioned above are given. As a special case, some results dealing with the corresponding matrix equations are also presented.