Lesson 4 of 10Article18 min
Span, Independence, Basis & Dimension
A subspace is closed under addition and scalar multiplication. Span{v₁,…,vₖ} is the smallest subspace containing those vectors.
Structure of subspaces
A subspace is closed under addition and scalar multiplication. Span{v₁,…,vₖ} is the smallest subspace containing those vectors.
- Column space Col(A): span of columns — range of x ↦ Ax.
- Null space Nul(A): solutions to Ax=0.
- Rank–nullity: rank(A) + dim Nul(A) = n for A m×n.