有限维线性空间中基的具体求法

Method of seeking basis in finite dimension linear space

m个n维(m<n)线性无关向量组,如何扩充为n维线性空间V的一组基,高等代数与线性代数教材中并没有给出具体有效的方法。为此,先把待扩充的向量组用线性空间V的坐标基线性表示,然后在其表示式的系数矩阵中寻找一个m阶非零子式,则可以立即得到由n-m个坐标向量和原向量组组成的n维线性空间V的一组基。

How can themlinearly independent vectors group in n dimensions linear spaces V be extended to the basis of linear spaces, the concrete and valid methods are not given in the higher algebra and linear algebra textbooks. For this purpose, the coordinate basis vectors at first may be linearly represented by the vectors group which is going to extend. Then we look for a m order non-zero subdeterminant in the coefficient matrix of the above representation formula. Thus we can obtain a basis in ndimension linearly space V by combining n--m coordinate vectors with the original vectors group.