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arXiv · 2006.15544

Application of quasideterminants to the inverse of block triangular matrices over noncommutative rings

Xuzhou Zhan
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Abstract

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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Xuzhou Zhan. 2020-06-28. Application of quasideterminants to the inverse of block triangular matrices over noncommutative rings. https://arxiv.org/abs/2006.15544

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