Short note on the perturbation of operators with dyadic products

Details Short note on the perturbation of operators with dyadic products Short note on the perturbation of operators with dyadic products

2008-10-07

arxiv.org/abs/0810.1201v1

Mathematics

Rings and Algebras

6 pages

Scientific paper

In this paper we use abstract vector spaces and their duals without any canonical basis. Some of our results can be extended to infinite dimensional vector spaces too, but here we consider only finite dimensional spaces. We focus on a general perturbation problem. Assume that $B:V\to V$ is a linear operator, which is perturbated to $B'=B+Q$. We examine the question how the determinant and the inverse change, because of this perturbation. In our approach the operator $Q$ is given as a sum of dyadic products $Q=\sum_{i=1}^{k}v_{i}\otimes p_{i}$, where $v_{i}\in V$ and $p_{i}\in V^{*}$. In this paper we derive an $m$-th order ($m\in\mathbb{N}$) approximation formula for $\det B'$ and $(B')^{-1}$, which gives the exact result if $m\geq k$.

Affiliated with

Also associated with

No associations

Rating

Short note on the perturbation of operators with dyadic products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Short note on the perturbation of operators with dyadic products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Short note on the perturbation of operators with dyadic products will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-557231