论文标题
在三角形的三角形矩阵上
On triangular similarity of nilpotent triangular matrices
论文作者
论文摘要
令$ b_n $（分别$ u_n $，$ n_n $）为$ n \ times n $ nosingular（resp。Unit，nilpotent）上三角矩阵。我们使用一种新颖的方法来探索$ n_n $中的$ b_n $ - 类似轨道。 $ b_n $下的$ a \ in $ b_n $ -simarlity的belitski \uı的规范形式在$ qu_n $中，其中$ q $是subpermunt的，以至于b_n qb_n $中的$ a \。使用图表表示和$ u_n $ -simurality动作稳定$ qu_n $，我们获得了Belitski \uı的规范形式的新属性，并提出了一种有效的算法，以找到Belitski \uı的规范形式。结果，我们在所有$ n_n $中构建了新的belitski \uı的规范形式，列出了所有belitski \uı的规范形式，价格为$ n = 7，8 $，并显示了3- nilpotent belitski \uı的示例中的$ n_n $ n_n $中的$ n_n $ n _n $ compameters $ nimuly pament cameters $ n _n $的$ \ pameters $ \ perageNorn and $ \ permatorateN.
Let $B_n$ (resp. $U_n$, $N_n$) be the set of $n\times n$ nonsingular (resp. unit, nilpotent) upper triangular matrices. We use a novel approach to explore the $B_n$-similarity orbits in $N_n$. The Belitski\uı's canonical form of $A\in N_n$ under $B_n$-similarity is in $QU_n$ where $Q$ is the subpermutation such that $A\in B_n QB_n$. Using graph representations and $U_n$-similarity actions stablizing $QU_n$, we obtain new properties of the Belitski\uı's canonical forms and present an efficient algorithm to find the Belitski\uı's canonical forms in $N_n$. As consequences, we construct new Belitski\uı's canonical forms in all $N_n$'s, list all Belitski\uı's canonical forms for $n=7, 8$, and show examples of 3-nilpotent Belitski\uı's canonical forms in $N_n$ with arbitrary numbers of parameters up to $\operatorname{O}(n^2)$.
