外积的推广及其性质和应用

Generalization of Outer Product and Application

引入新记号,定义n(n≥2)维外积,得到正交向量的一些新性质,从而把线性无关组正交化过程转为计算行列式的代数余子式,由于回避了分数运算,故可在计算机上得到精确结果.此外通过外积,可扩充n维空间正交基,并把n维直线方程的一般式化为标准式.

In this paper , by introducing n-dimensional outer product , some new theorems of orthogonal vectors are presented , which transfer the process of orthogonalization into the calculation of cofactors of determinant .Another benefit of this is that , because of avoiding fractions , the orthogonalization can be more accurate in computing .In addition ,by using the outer product ,a method of expanding orthogonal basis is given , and the general equation of a straight line on n-dimensional space can be converted into the standard form .