Vector Linear Independence

Description:

• A collection $x^{(}1),...,x^{(}m)$ of vectors in a vector space $X$ is said to be linearly independent if no vector in the collection can be expressed as a Linear Combination of the others.
  • ie, $\sum _{i=1}^m{\alpha }_i{x}^{(i)}=0⟹\forall {\alpha }_i=0$
    • because there is no way for 1 vector to go to another vector as they are parallel
  • meaning the linear combination of them is always 0
• They are linearly dependence, otherwise, if one vector doesnt help expanding the span of the collection of vectors