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。

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 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。

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。