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Upper bounds of spectral radius of symmetric matrices and graphs.
- Source :
-
Linear Algebra & its Applications . Feb2024, Vol. 682, p152-163. 12p. - Publication Year :
- 2024
-
Abstract
- The spectral radius ρ (A) is the maximum absolute value of the eigenvalues of a matrix A. In this paper, we establish some relationship between the spectral radius of a symmetric matrix and its principal submatrices, i.e., if A is partitioned as a 2 × 2 block matrix A = ( 0 A 12 A 21 A 22 ) , then ρ (A) 2 ≤ ρ 2 2 + θ ⁎ , where θ ⁎ is the largest real root of the equation μ 2 = (x − ν) 2 (ρ 2 2 + x) and ρ 2 = ρ (A 22) , μ = ρ (A 12 A 22 A 21) , ν = ρ (A 12 A 21). Furthermore, the results are used to obtain several upper bounds of the spectral radius of graphs, which strengthen or improve some known results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SYMMETRIC matrices
*MATHEMATICAL bounds
*ABSOLUTE value
*EIGENVALUES
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 682
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 174060262
- Full Text :
- https://doi.org/10.1016/j.laa.2023.11.008