In other words, the column space is the span of the columns of your matrix.

换句话说 列空间就是矩阵的列张成的空间。

Notice, the zero vector will always be included in the column space.

注意 零向量总是包含在列空间中。

The idea of column space lets us understand when a solution even exists.

列空间的概念让我们理解解何时存在。

So a more precise definition of rank would be that it's the number of dimensions in the column space.

所以秩的一个更精确的定义是它是列空间中的维数。

This video is No Exception, describing the concepts of inverse matrices, column space, rank and, uh no, space through that lens.

这个视频是《无一例外》，描述了逆矩阵，列空间，秩，还有，不，通过这个镜头的空间。

This set of all the possible outputs for your matrix, whether it's a line, a plain 3D space, whatever, is called the column space of your matrix.

这个矩阵的所有可能输出的集合 无论是一条直线 一个普通的三维空间 无论什么 都被称为矩阵的列空间。

But the matrix is still full rank, since the number of dimensions in this column space is the same as the number of dimensions of the input space.

但是这个矩阵仍然是满秩的 因为这个列空间的维数和输入空间的维数是一样的。

In the language of last video, the column space of this matrix, the place where all the vectors land, is a two D plane slicing through the origin of three D space.

用上个视频的语言来说 这个矩阵的列空间 所有向量的落点 是一个二维平面 穿过三维空间的原点。

It's that you come away with a strong intuition for inverse matrices, column space and no space, and that those intuitions make any future learning that you do more fruitful.

你会对逆矩阵 列空间和无空间有很强的直觉 这些直觉会让你以后的学习更有成效。