Linear combination = 기본변형 (eg. v1, 3v1-1v2+1/2v3)
Span: set of all linear combinations of the vectors (기본변형으로 만들 수 있는 모든 벡터들)
Linear combination을 통한 matrix multiplication의 inner product & outer product 계산 방법 존재
Linearly independent: only one solution (trivial solution)
Linearly dependent: other nontrivial solutions / linearly dependent set produces multiple possible linear combinations.
Subspace: a subset of R^n closed under linear combination
==> a subspace is always represented as Span{v1, …, vp}
Basis of a subspace: set of vectors that satisfies (1) fully spans the given subspace H (2)linearly independent
•eg. H = Span{v1, v2, v3} è Span{v1, v2} forms a plane, but v3=2v1+3v2 ∈ Span{v1, v2} è {v1, v2} is a basis of H, but not {v1, v2, v3} nor {v1} is a basis.
•Basis is not unique
•BUT, 어떤 종류의 basis라도 그 basis에 있는 벡터의 갯수=dimension은 unique!)
Column Space
(eg. Linearly dependent columns)
Rank of matrix A = dim Col A
Linear Tranformation(선형 변환)
