Those of you who watch Chapter Two will recognize this as meaning that the columns of the matrix are linearly dependent.
看过第二章的人会知道这意味着矩阵的列向量是线性相关的。
Linear algebra
Whenever this happens, where you have multiple vectors and you could remove one without reducing the span, the relevant terminology is to say that they are linearly dependent.
If the vectors that I had N-J had land on, are linearly dependent, which, if you recall from last video, means that one is a scaled version of the other.
如果N-J所落的向量 是线性相关的 如果你还记得上个视频 这意味着一个向量是另一个向量的缩放版本。
Linear algebra
It means that the linear transformation squishes all of two d space on to the line where those two vectors sit, also known as the one dimensional span of those two linearly dependent vectors.
The vectors in a set are said to be linearly independent if the equation
can only be satisfied by for . This implies that no vector in the set can be represented as a linear combination of the remaining vectors in the set. In other words, a set of vectors is linearly independent if the only representations of 0 as a linear combination of its vectors is the trivial representation in which all the scalars ai are zero.