Module: Bases and dimension

Learning Outcomes

Bases and Dimension

• Basis = Maximal linearly independent set
• Natural coordinate basis for ${\mathbb R}^n$: columns of $I_n$
• Dimension of a linear space = Size of the basis
• Identify basis for fundamental spaces of $A$ using (pivot) rows/columns of $A$, as well as non-zero rows/cols of rref($A$) and rref($A^T$)
• Dimension of all fundamental spaces of $A$ in terms of rank and shape of $A$

Readings

Experiential Learning