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。

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。