Asymptotically exact spectral estimates for left triangular matrices

Abstract

For a family of $n\ast n$ 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.

7 pages, LaTeX