积和式及其计算
摘要
本文给出了积和式的定义如下:设 是 × 矩阵( ),则称和式 为 的积和式(permanent),这里 表示{ }中所有 元排列的集合。
本文中详细阐述了积和式、 矩阵积和式的1些性质。在积和式的计算方面,阐述了利用Ryser定理计算积和式 的传统方法;利用正行列式得到两类 矩阵积和式,并给出其两种类型的组合应用,其后,利用正行列式建立了计算积和式 的另1种计算理论;最后还给出了关于双随机矩阵的两个问题的计算证明。
关键词:积和式;Ryser定理; 矩阵;双随机矩阵;应用
Abstract
Define the permanent as follows: It is supposed that is × matrix( ),so claim the permanent as the permanent of , Here is all —Permutation of{ }.
The text described some properties of permanent、 matrix permanent 。At calculation for permanent, it described the tradition method of utilization Ryser theorem to calculate permanent ,Utilize the positive determinant to receive two kinds of matrix permanent, Provide its two types association application; Thereafter, it set up another kind of calculation theory of Calculation permanent that still utilize the positive determinant; finally, provide the identifications of two questions about bistochastic matrix.
Keywords:Permanent; -matrix;Ryser theorem;bistochastic matrix; Application.
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