Vectors and spaces

Vectors

Linear combinations and spans

Linear dependence and independence

Subspaces and the basis for a subspace

Vector dot and cross products

Matrices for solving systems by elimination

Null space and column space

Matrix transformations

Functions and linear transformations

Linear transformation examples

Transformations and matrix multiplication

Inverse functions and transformations

Finding inverses and determinants

More determinant depth

Transpose of a matrix

Alternate coordinate systems (bases)

Orthogonal complements

Orthogonal projections

Change of basis

Orthonormal bases and the Gram-Schmidt process

Eigen-everything

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