论文标题
在非交通环上的块三角形矩阵的倒数中施用了准固定剂
Application of quasideterminants to the inverse of block triangular matrices over noncommutative rings
论文作者
论文摘要
给定一个块三角矩阵$ m $在具有可逆对角线块的非交通戒指上，这项工作给出了两个新的表示其反向$ m^{ - 1} $的新表示。 $ m^{ - 1} $的每个块元素通过$ m $的subsiDeTermants与Block Hessenberg类型明确表示。因此，获得了每个反向块的另一个表示形式，这是在$ m^{ - 1} $的块之间与多个项的复发关系。后一个结果使我们能够对$ M $的反向计算进行偏置矩形扰动分析。举例说明了我们结果的有效性。
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.
