What we want is a non zero eigenvector.

我们要的是一个非零特征向量。

That means there's a non zero vector V, such that a minus land at times the identity, times V equals the zero vector.

这意味着存在一个非零向量V 使得a-land乘以恒等式 乘以V等于零向量。

Let's start with the most likely case, where the determinant is non zero, meaning space does not gets pushed into a zero area region.

让我们从最可能的情况开始 行列式是非零的 这意味着空间不会被推到零面积区域。

In the language of the last video, we subdivide into the cases where a has zero determinant and the case where a has non zero determinant.

在上一集视频中 我们将矩阵a的行列式为零的情况和矩阵a的行列式为非零的情况进行细分。

But for this video, will limit our view to the case of a non zero determinant, meaning the outputs of this transformation still span the full dimensional space that it started in.

但是在这个视频中 我们将把视野限制在非零行列式的情况下 这意味着这个变换的输出仍然张成了它开始时所在的全维空间。

As long as the transformation A doesn't squish all of space into a lower dimension, meaning its determinant is non zero, there will be an inverse transformation, a inverse with the property that if you 1st do a then you do a inverse.

只要变换A没有把所有空间压缩到更低的维度 也就是说它的行列式非零 就会有一个逆变换 这个逆的性质是如果你先做A 然后再做逆。