行列式理论中两个主要结论的推广

Generalizations of Two Important Results in the Theory of Determinant

文[1]把行列式的概念推广为行式、列式,并且得出一系列性质.本文主要给出两个新结果:一个是推广代数余子式的概念,得到行式依行、列式依列展开定理及其推论;另一个是把Cramer法则推广到方程个数不少于未知量个数的情况.

As a generalization of the concept of determinant, two concepts of row determinant and column-determinant have been established in the paper [l]. Then the writer obtains two new results: one generalizes the concept of cofactor of a determinant to row determinant and column determinant, and gives their expansion formulae with respect to a row and a column respectively as well as some corollaries; the other genera lizes the Cramer formula to a system of m linear equations with m not less than the number of unknowns