On the spectrum of noisy blown-up matrices
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-04-01
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| Series: | Special Matrices |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/spma-2020-0010 |
| Summary: | 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. |
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| ISSN: | 2300-7451 |