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# Linear Algebra with Applications

## Abstract vector spaces in theory and application.

Linear algebra plays a crucial role in many branches of applied science and pure mathematics. This course covers the core ideas of linear algebra and provides a solid foundation for future learning.

Using geometric intuition as a starting point, the course journeys into the abstract aspects of linear algebra that make it so widely applicable. By the end you'll know about vector spaces, linear transformations, determinants, eigenvalues & eigenvectors, tensor & wedge products, and much more.

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490+
1. 1

### Introduction to Vector Spaces

1. #### What is a Vector?

Discover the true nature of vectors.

2. #### Waves as Abstract Vectors

Take a visual tour of vector spaces.

3. #### Why Vector Spaces?

Experience the power of abstraction.

2. 2

### System of Equations

1. Included with

#### The Gauss-Jordan Process I

Gain experience with systems of equations through traffic planning.

2. Included with

#### The Gauss-Jordan Process II

Learn a surefire method for cracking any set of linear equations.

3. Included with

#### Application: Markov Chains I

Apply your Gauss-Jordan skills to a classic probability problem.

3. 3

### Vector Spaces

1. Included with

#### Real Euclidean Space I

Learn about important abstract concepts in a familiar setting.

2. Included with

#### Real Euclidean Space II

Lay the foundation for building vector spaces.

3. Included with

#### Span & Subspaces

Develop a quick means for generating vector spaces.

4. Included with

#### Coordinates & Bases

Condense common vector spaces with bases.

4. 4

### Linear Transformations

1. Included with

#### What Is a Matrix?

Free your mind from viewing matrices as just arrays of numbers.

2. Included with

#### Linear Transformations

Come full circle and connect linear maps back to matrices.

3. Included with

#### Matrix Products

Find out one way of multiplying matrices together.

4. Included with

#### Matrix Inverses

Learn when it's OK to divide by a matrix.

5. 5

### Multilinear Maps & Determinants

1. Included with

#### Bivectors

Take the first step towards determinants with bivectors.

2. Included with

#### Trivectors & Determinants

Evaluate determinants like a pro with trivectors.

3. Included with

#### Determinant Properties

Gain experience with the most important properties of determinants.

4. Included with

#### Multivector Geometry

Learn about the visual aspects of multivectors.

6. 6

### Eigenvalues & Eigenvectors

1. Included with

#### Application: Markov Chains II

Discover eigenvectors by rethinking a classic probability problem.

2. Included with

#### Eigenvalues & Eigenvectors

Learn the essentials of eigenvalues & eigenvectors.

3. Included with

#### Diagonalizability

Restructure square matrices in the most useful way imaginable.

4. Included with

#### Normal Matrices

When can a matrix be diagonalized?

7. 7

### Inner Product Spaces

1. Included with

#### Inner Product Spaces

Extend familiar geometric tools to abstract spaces.

2. Included with

#### Gram-Schmidt Process

Practice making your very own orthonormal bases.

3. Included with