linear independence
선형 대수
Linear independence
Definition
- Dependence: one of the vectors in the set can be written as a linear combination of the others.
- Independence: ⫬ dependence
Theorem
S = \({v_1, v_2, ..., v_n}\)
\(S\) is linearly dependent ⟺ ∃(\(c_i\) is not 0) \(c_1v_1 + c_2v_2 + ... + c_nv_n = 0\) is \(c_1 = c_2 = ... = c_n = 0\).
- if \(c_1 = c_2 = ... = c_n = 0\), then \(S\) is linearly independent.