**What is Linear Algebra?**

Quick Introduction

The following video provides an outline of all the topics you would expect to see in a typical

**College Linear Algebra**class (i.e., Matrix Algebra).

All of the topics are covered in detail in our Online Linear Algebra Course.

The online course contains:

- Full Lectures –
*Designed to boost your test scores.* - 150+ HD Video Library –
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*Never worry about missing a class again.* - Practice Exams –
*Ensure you’re ready for your finals.*

## Linear Algebra Overview

Linear Algebra Overview

The following sections provide links to our complete lessons on all Linear Algebra topics.

Also, be sure to check out our FREE calculus tutoring videos and read our reviews to see what we’re like.

## Linear Equations

8 Videos 61 Examples

- Systems of Linear Equations
- Row Reduction and Echelon Forms
- Vector Equations
- The Matrix Equation Ax=b
- Solution Sets of Linear Systems
- Linear Independence
- Linear Transformations and the Matrix of a Linear Transformation
- Applications of Linear Systems and Linear Models in Business, Science and Engineering

## Matrix Algebra

6 Videos 43 Examples

- Matrix Operations and Determinants
- The Inverse of a Matrix
- Characterizations of Invertible Matrices
- Partitioned Matrices
- Matrix Factorization (LU Decomposition)
- Applications to Computer Graphics

## Determinants

2 Videos 22 Examples

- Properties to Determinants
- Cramer’s Rule, Volume, and Linear Transformations

## Vector Spaces

8 Videos 61 Examples

- Vector Spaces and Subspaces
- Null Spaces, Column Spaces, Row Spaces and Linear Transformations
- Linearly Independent Sets; Bases
- Coordinate Systems
- The Dimension of a Vector Space
- Rank
- Change of Basis
- Applications to Markov Chains

## Eigenvalues and Eigenvectors

5 Videos 20 Examples

- Eigenvectors and Eigenvalues
- The Characteristic Equation
- Diagonolization
- Eigenvectors and Linear Transformations
- Complex Eigenvalues

## Orthogonality and Least Squares

7 Videos 52 Examples

- Inner Product, Length, and Orthogonality
- Orthogonal Sets
- Orthogonal Projections
- The Gram-Schmidt Process and QR Factorization
- Least-Squares Problems
- Applications to Linear Models (Line of Regressions)
- Inner Product Spaces

## Symmetric Matrices and Quadratic Forms

2 Videos 14 Examples

- Diagonalization of Symmetric Matrices
- Quadratic Forms

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