You start with that change of basis matrix that translates jennifer's language into ours.

你从基底变换矩阵开始把jennifer的语言转换成我们的语言。

So as a last step, apply the inverse change of basis matrix multiplied on the left, as usual, to get the transformed vector.

最后一步 应用基的逆变换矩阵乘以左边 像往常一样 得到变换后的向量。

But now, in jennifer's language, since we could do this with any vector written in her language, 1st applying the change of basis, then the transformation, then the inverse change of basis.

但是现在 在jennifer的语言中 因为我们可以用她的语言来做这个 首先应用基的变换 然后是变换 然后是基的逆变换。

I talked about change of basis last video, but I'll go through a super quick reminder here of how to express a transformation currently written in our coordinate system into a different system.

上个视频我讲了基的变换 但是我要快速地讲一下如何把当前坐标系中的变换表示成另一个坐标系中的变换。

In practice, especially when you're working in more than two dimensions, you'd use a computer to compute the matrix that actually represents this inverse, in this case, the inverse of the change of basis.

在实践中 特别是在二维以上的情况下 你会用计算机来计算这个矩阵来表示这个逆 在这种情况下 就是基底变换的逆。

Most important here is that you know how to think about matrices as linear transformations, but you also need to be comfortable with things like determinants, linear systems of equations and change of basis.

这里最重要的是你知道如何把矩阵看作线性变换 但你也需要熟悉行列式 线性方程组和基底变换。