Linear Independence #
A set of vectors is linearly independent if none of them can be written as a linear combination of the others.
\[ c_1\mathbf{v}_1 + \cdots + c_k\mathbf{v}_k = \mathbf{0} \;\Rightarrow\; c_1=\cdots=c_k=0 \]Independence means each vector adds new information.
Why it matters #
- Detects redundancy
- Connects to rank and basis