For a family of $n*n$ left triangular matrices with binary entries we deriveasymptotically exact (as $n\to\infty$) representation for the completeeigenvalues-eigenvectors problem. In particular we show that the dependence ofall eigenvalues on $n$ is asymptotically linear for large $n$. A similar resultis obtained for more general (with specially scaled entries) left triangularmatrices as well. As an application we study ergodic properties of a family ofchaotic maps.
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机译：对于具有二元项的$ n * n $左三角矩阵族，我们针对完全特征值-特征向量问题渐近精确地表示为（$ n \ to \ infty $）。特别地，我们表明，对于大的$ n $，所有特征值对$ n $的依赖性都是渐近线性的。对于更通用的（带有特殊比例的条目）左三角矩阵也获得了相似的结果。作为一种应用，我们研究了一系列混沌图的遍历性质。
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