On the spectrum of noisy blown-up matrices

Abstract

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.

Keywords

• eigenvalue
• symmetric matrix
• blown-up matrix
• random matrix
• perturbation of a matrix
• singular value
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