The spectral radius of matrix continuous refinement operators
โ Scribed by Victor Didenko; Wee Ping Yeo
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 394 KB
- Volume
- 33
- Category
- Article
- ISSN
- 1019-7168
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๐ SIMILAR VOLUMES
Define the sign-real spectral radius of a real n ร n matrix A as ฯ s 0 (A) = max SโS ฯ 0 (SA), where ฯ 0 (A) = max{|ฮป|; ฮป a real eigenvalue of A} is the real spectral radius of A and S denotes the set of signature matrices, i.e. S = {S; |S| = I}, the absolute value of matrices being meant entrywise.
We develop lower bounds for the spectral radius of symmetric, skew-symmetric, and arbitrary real matrices, Our approach utilizes the well-known Leverrier-Faddeev algorithm for calculating the coefficients of the characteristic polynomial of a matrix in conjunction with a theorem by Lucas which state