00-346 Michael Blank

Asymptotically exact spectral estimates for left triangular matrices (14K, LATeX 2e) Sep 8, 00

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Abstract. For a family of $n*n$ left triangular matrices with binary entries we derive asymptotically exact (as $n\to\infty$) representation for the complete eigenvalues-eigenvectors problem. In particular we show that the dependence of all eigenvalues on $n$ is asymptotically linear for large $n$. A similar result is obtained for more general (with specially scaled entries) left triangular matrices as well. As an application we study ergodic properties of a family of chaotic maps.

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