拟行列式在非交换环上分块三角形矩阵逆中的应用
Application of quasideterminants to the inverse of block triangular matrices over noncommutative rings
摘要：
给定对角块可逆的非交换环上的块三角形矩阵$M$，给出了它的逆矩阵$M^{-1}$的两种新表示. $M^{-1}$的每个块元素通过具有块Hessenberg型的$M$的子矩阵的拟行列式显式地表示。相应地，获得了每个逆块的另一种表示，该表示是根据$M^{-1}$的块之间的多个项的递归关系。后者的结果使我们能够执行非对角矩形扰动分析的逆计算的$M$。最后通过一个例子说明了所得结果的有效性.
英文摘要：
Given a block triangular matrix $M$ over a noncommutative ring with invertible diagonal blocks, this work gives two new representations of its inverse $M^{-1}$. Each block element of $M^{-1}$ is explicitly expressed via a quasideterminant of a submatrix of $M$ with the block Hessenberg type. Accordingly another representation for each inverse block is attained, which is in terms of recurrence relationship with multiple terms among blocks of $M^{-1}$. The latter result allows us to perform an off-diagonal rectangular perturbation analysis for the inverse calculation of $M$. An example is given to illustrate the effectiveness of our results.
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