Khan Academy

Dimension of the null space or nullity (K-A)

Introduction to the null space of a matrix (K-A)

Matrix vector products (K-A)

Null space 2: Calculating the null space of a matrix (K-A)

Null space 3: Relation to linear independence (K-A)

Null space and column space basis (K-A)

Proof: Any subspace basis has same number of elements (K-A)

Basis of a subspace (K-A)

Showing relation between basis cols and pivot cols (K-A)

Linear subspaces (K-A)

Showing that the candidate basis does span C(A) (K-A)

Visualizing a column space as a plane in R3 (K-A)

Cross product introduction (K-A)

Defining a plane in R3 with a point and normal vector (K-A)

Defining the angle between vectors (K-A)

Distance between planes (K-A)

Dot and cross product comparison/intuition (K-A)

Normal vector from plane equation (K-A)

Point distance to plane (K-A)

Proof of the Cauchy-Schwarz inequality (K-A)

Proof: Relationship between cross product and sin of angle (K-A)

Proving vector dot product properties (K-A)

Vector dot product and vector length (K-A)

Adding vectors algebraically & graphically (K-A)

Vector triangle inequality (K-A)