In general, you should think of linear transformations as keeping grid lines parallel and evenly spaced.

一般来说 您应该将线性变换视为保持网格线平行且间距均匀。

This follows from the fact that grid lines remain parallel and evenly spaced.

这源于网格线保持平行和均匀间隔的事实。

Thinking about grid lines remaining parallel, unevenly spaced is a little bit messy due to all of the squishification happening here.

考虑到网格线保持平行 由于这里发生了所有的挤压 不均匀的间隔有点乱。

One, always moving the rest of space in such a way that keeps grid lines parallel and evenly space.

第一 始终移动剩余的空间 使网格线保持平行和均匀的空间。

But the direction of her axes and the spacing of her grid lines will be different depending on her choice of basis.

但是她的轴的方向和网格线的间距会根据她选择的基底而不同。

I'll extend these take marks to make grid lines, but right now, they'll actually get a little bit in the way.

我将把这些take标记扩展成网格线 但现在 它们实际上有点碍事。

Again, what makes one of these linear is that grid lines remain parallel and evenly spaced, and that the origin maps to the origin.

同样 使这些线成为线性的是网格线保持平行且均匀间隔 原点映射到原点。

To sum up, linear transformations are a way to move around space such that grid lines remain parallel and evenly spaced, and such that the origin remains fixed.

总而言之 线性变换是一种在空间中移动的方法 使得网格线保持平行和均匀间隔 并且原点保持固定。

The idea of grid lines remaining parallel and evenly spaced, that I've talked about in past videos is really just an illustration of what these two properties mean in the specific case of points in two D space.

网格线保持平行和等距的概念 我在过去的视频中讲过实际上只是说明了这两个性质在二维空间中点的特定情况下的意义。

We can visualize this by smashing around all the points in three dimensional space, as represented by a grid, in such a way that keeps the grid lines parallel and evenly spaced, and which fixes the origin in place.

我们可以把三维空间中的所有点都打碎 用网格表示 使网格线保持平行和均匀间隔 并固定原点。