Michael Blank
Asymptotically exact spectral estimates for left triangular matrices
(14K, LATeX 2e)
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.