**What you will learn from this course?**

Vectors: Vectors and spaces

– Linear combinations and spans: Vectors and spaces

– Linear dependence and independence: Vectors and spaces

– Subspaces and the basis for a subspace: Vectors and spaces

– Vector dot and cross products: Vectors and spaces

– Matrices for solving systems by elimination: Vectors and spaces

– Null space and column space: Vectors and spaces

Matrix transformations

– Functions and linear transformations: Matrix transformations

– Linear transformation examples: Matrix transformations

– Transformations and matrix multiplication: Matrix transformations

– Inverse functions and transformations: Matrix transformations

– Finding inverses and determinants: Matrix transformations

– More determinant depth: Matrix transformations

– Transpose of a matrix: Matrix transformations

Alternate coordinate systems (bases)

– Orthogonal complements: Alternate coordinate systems (bases)

– Orthogonal projections: Alternate coordinate systems (bases)

– Change of basis: Alternate coordinate systems (bases)

– Orthonormal bases and the Gram-Schmidt process

– Eigen-everything: Alternate coordinate systems (bases)

**Certification :**No

**Time to complete :**1 week

**Cost :**Free

**Course Level :**Beginner

**Language :**English