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1 Overview
1.1 Intuition
- If you have a vector list \(v\) that is a linear combination of vectors in \(V\), or equivalently,
- \[v = a_1v_1 + ... + a_mv_m \text{where} v_1, ..., v_m \in V\]
- And those choices of \(a_1, ..., a_m\) are unique, then this is a linear independence? ## #definition linearly independent > - The empty list \(()\) is linearly independent > - A list \(v_1, ..., v_m\) of vectors in \(V\) is called linearly independent if the only choice of \(a_1, ..., a_m \in F\) that makes \(a_1v_1 + ... + a_mv_m\) equal \(0\) is \(a_1 = ... = a_m = 0\)
- ^^^ what the heck is that last part about everything equaling \(0\)?? #todo-exr0n KBe20math530floQuestions