The limit of the spectral radius of block Toeplitz matrices with nonnegative entries
✍ Scribed by L. Elsner; S. Friedland
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2000
- Tongue
- English
- Weight
- 323 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0378-620X
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📜 SIMILAR VOLUMES
Let M + n be the set of entrywise nonnegative n × n matrices. Denote by r(A) the spectral radius (Perron root) of A ∈ M + n . Characterization is obtained for maps f : In particular, it is shown that such a map has the form for some S ∈ M + n with exactly one positive entry in each row and each co
The Toeplitz (or block Toeplitz) matrices S(r)=[s j&k ] r k, j=1 , generated by the Taylor coefficients at zero of analytic functions .(\*)= s0 2 + p=1 s & p \* p and (+)= s0 2 + p=1 s p + p , are considered. A method is proposed for removing the poles of . and or, in other words, for replacing S( )
## We prove the spectral radius inequality ρ(A for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality A • B ρ(A T B) for nonnegative matrices, which improves Schur's classical inequality , where • denotes the spectral norm. We also give counterexamples to two conject