探讨方阵的因子分解与其零度之关系

Studies on the relationship between the factorization of a square matrix and its nullities

本文讨论在一般数域F上任一方阵的因子分解与零度之关系，论证了一个方阵化为两个或两个以上对称矩阵的乘积时，其零度之间必须满足的条件，并给出矩阵进行因子分解的实际方法．

In this paper we discuss the relationship between the factorization of a square matrix over a field F and its nullify, expound and prove the necessary conditions for the relation between the nullities of the derived symmetric matrices when a square matrix is changed into the product of two or over two symmetric matrices, and present pratical methods for the factorization of a matrix.