论文标题
正定矩阵的规范形式
A Canonical Form for Positive Definite Matrices
论文作者
论文摘要
我们表现出一种明确的，确定性的算法，用于在单形成积分转换下找到正定矩阵的规范形式。我们使用简短矢量的特征集和分区式图形软件。该算法以许多在尺寸$ n $中指数的算术操作运行，但是它比基于Minkowski降低的规范形式更实用，更有效。
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension $n$, but it is practical and more efficient than canonical forms based on Minkowski reduction.
