Learn Linear Algebra with Applications

Description

In this course, you will :

• Learn about the true nature of vectors.
• Discover the power of abstraction.
• Through traffic planning, you can gain experience with equation systems.
• Learn a foolproof method for solving any set of linear equations.
• Learn about important abstract concepts in a comfortable environment.
• When is it appropriate to divide by a matrix?
• Learn about the most important determinant properties.
• Discover the visual properties of multivectors.
• By rethinking a classic probability problem, you can find eigenvectors.
• Discover the fundamentals of eigenvalues and eigenvectors.

Syllabus :

1. Introduction to Vector Spaces

• What is a Vector?
• Waves as Abstract Vectors
• Why Vector Spaces?

 

2. System of Equations

• The Gauss-Jordan Process 
• Application: Markov Chains 

 

3. Vector Spaces

• Real Euclidean Space 
• Span & Subspaces
• Coordinates & Bases

 

4. Linear Transformations

• What Is a Matrix?
• Linear Transformations
• Matrix Products
• Matrix Inverses

 

5. Multilinear Maps & Determinants

• Bivectors
• Trivectors & Determinants
• Determinant Properties
• Multivector Geometry

 

6. Eigenvalues & Eigenvectors

• Application: Markov Chains
• Eigenvalues & Eigenvectors
• Diagonalizability
• Normal Matrices

 

7. Inner Product Spaces

• Inner Product Spaces
• Gram-Schmidt Process
• Least Squares Regression
• Singular Values & Vectors

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