单对合矩阵之积

本文解决的问题是,1°.找出了一个条件(*),它是将一个具行列式±1的n(>1)阶矩阵A表为k(1≤k≤n)个单对合矩阵之积的必要条件;2°。证明了对于特征为2的域F,条件(*)为具行列式为1的矩阵A表为不多于两个单对合矩阵之积的充要条件;3°。证明了当域F的阶为2时,条件(*)为A可表为个数不超过k的单对合矩阵之积的充要条件。

Product of Simple lnvolutory Matrices

In this paper the problems are solved as follows, 1 °. A condition (*) which is a necessary condition for that a matrix A with detA=± 1, can be represented as the product of k ( 1 ≤k≤n) simple involutory matrices. 2° It is proved that the condition (*) is also a sufficient condition for A when k= 2 and the characterization of a field is 2 . 3°. It is also shown that the condition (*) is a sufficient and necessary condition for a matrix A which can be represented as the product of not more than K simple involutory matrices when the order of a field F is 2.