Linear Algebra

Compositions of Linear Transformations 1

Lin Alg: Orthogonal matrices preserve angles and lengths

Lin Alg: Finding projection onto subspace with orthonormal basis example

Compositions of Linear Transformations 2

Lin Alg: Representing vectors in Rn using subspace members

Determining whether a transformation is onto

Linear Algebra: Matrix Product Examples

Linear Alg: Projection is closest vector in subspace

Linear Algebra: Subspace Projection Matrix Example

More on Matrix Addition and Scalar Multiplication

Null Space 2: Calculating the null space of a matrix

Distributive Property of Matrix Products

Defining a plane in R3 with a point and normal vector

Expressing a Projection on to a line as a Matrix Vector prod

Null Space 3: Relation to Linear Independence

Linear Algebra: Parametric Representations of Lines

Showing relation between basis cols and pivot cols

Preimage of a set

Matrix Product Associativity

Matrix Vector Products as Linear Transformations