I have seen the paper: W. Li and J.-X. Chen,
The eigenvalue perturbation bound for arbitrary matrices
, J. Comput.Math. (2006), 141–148 in this regard. Are there any more? Ren-Cang Li (2014). "Matrix Perturbation Theory". In Hogben, Leslie. Handbook of linear algebra (Second ed.) is another survey. Can anybody help me to have more on this topic?
Is P an arbitrary matrix? If so, you should try proving that |λ−λi|≤||δA|||λ−λi|≤||δA||. Assuming AA is full rank, here's a way to do this - Let the eigenvector corresponding to λλ be uu. Note that {vi}i=1,…,n{vi}i=1,…,n is a basis. Now expand the equation (A+δA)u=λu(A+δA)u=λu in terms of the aforementioned basis, rearrange a little, and take inner product with vivi.
Dear Jackson
My matrix is arbitrary. If you could send your suggestion in a pdf form it would be helpful for me as the answer written here is not completely readable. My mail id: [email protected]
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