On the spectrum of noisy blown-up matrices

Special Matrices

Fazekas István¹  Pecsora Sándor¹ 

[1] University of Debrecen, Faculty of Informatics, P.O. Box 400, 4002 Debrecen, Hungary;

关键词: eigenvalue;    symmetric matrix;    blown-up matrix;    random matrix;    perturbation of a matrix;    singular value;    15a18;    15a52;    60f15;   

DOI  :  10.1515/spma-2020-0010

来源: DOAJ

【 摘 要 】

We study the eigenvalues of large perturbed matrices. We consider a pattern matrix P, we blow it up to get a large block-matrix Bn. We can observe only a noisy version of matrix Bn. So we add a random noise Wn to obtain the perturbed matrix An = Bn + Wn. Our aim is to find the structural eigenvalues of An. We prove asymptotic theorems on this problem and also suggest a graphical method to distinguish the structural and the non-structural eigenvalues of An.

【 授权许可】

Unknown