Now, this will always be true if V itself is the zero vector, but that's boring.

现在 如果V本身是0向量 这个总是成立的 但这很无聊。

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。

When their perpendicular meaning, the projection of one onto the other, is the zero vector, their dot product is zero.

当它们垂直的意思 一个向量在另一个向量上的投影 是零向量时 它们的点积是零。

For a full rank transformation, the only vector that lands at the origin is the zero vector itself.

对于一个全秩变换 唯一落在原点的向量是零向量本身。

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。

When V happens to be the zero vector, the no space gives you all of the possible solutions to the equation.

当V是零向量时 无空间给出了方程的所有可能解。

So what we now have is a new matrix, A minus lambder, times the identity, and we're looking for a vector V such that this new matrix times V gives the zero vector.

现在我们有了一个新矩阵 a- 乘以单位矩阵 我们在寻找一个向量V使得这个新矩阵乘以V得到0向量。