Linear Independence - Linearly Independent - Linear Dependence - Linearly Dependent
- a set of vectors is said to be linearly independent if there exists NO non-trivial linear combination of the vectors that equals the zero vector
- a set of vectors is said to be linearly dependent if there exists a non-trivial linear combination of the vectors that equals the zero vector
Linear Independence - Definition
A set of vectors {𝑣1, 𝑣2, …, 𝑣𝑘} from a vector space 𝑉 is linearly independent if there do NOT exist scalars {𝛼1, 𝛼2, …, 𝛼𝑘}, not all zero such that:
- 𝛼1𝑣1 + 𝛼2𝑣2 + … + 𝛼𝑘𝑣𝑘 = zero vector