如何检查n个n个向量是否线性独立? [英] How to check if m n-sized vectors are linearly independent?

问题描述

免责声明
这并不是严格意义上的编程问题，但是大多数程序员迟早都必须处理数学(尤其是代数)，因此我认为答案将来可能会对其他人有用.

Disclaimer
This is not strictly a programming question, but most programmers soon or later have to deal with math (especially algebra), so I think that the answer could turn out to be useful to someone else in the future.

现在有问题
我正在尝试检查维度n的m个向量是否线性独立.如果m == n，则可以使用向量构建矩阵，然后检查行列式是否为！= 0.否?

Now the problem
I'm trying to check if m vectors of dimension n are linearly independent. If m == n you can just build a matrix using the vectors and check if the determinant is != 0. But what if m < n?

有任何提示吗?

另请参见此视频讲座.

推荐答案

构造向量矩阵(每个向量一行)，并执行

Construct a matrix of the vectors (one row per vector), and perform a Gaussian elimination on this matrix. If any of the matrix rows cancels out, they are not linearly independent.

平凡的情况是当m> n时，在这种情况下，它们不能是线性独立的.

The trivial case is when m > n, in this case, they cannot be linearly independent.

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