Limit Jordan normal form of large triangular matrices over a finite field
For any upper triangular matrix \(X\) over the finite field \(\mathbb{F}_q\), which contains \(q\) elements \((X= (x_{ij}) \in\text{Mat}_n(\mathbb{F}_q)\) and \(x_{ij} = 0\), \(i\geq j)\), the author defines the type of \(X\) as the partition \(l= \{l_1\geq \cdots\geq l_r\}\) of \(n\) such that the orders of the Jordan blocks of \(X\) are equal to \(l_1\geq \cdots\geq l_r\). The paper is devoted to the study of the distribution of the above matrices with respect to the type as \(n\to\infty\).
scientific article; zbMATH DE number 923591