Learn Introduction to Linear Algebra

Description

In this course, you will :

• Learn a general algorithm for solving equation systems.
• Learn about the concept of a space within a space.
• Discover how to identify redundant vectors.
• What is the unit of measurement for the size of a vector space?
• Discover how to convert vectors into... other vectors.
• Discover the intricate relationship between linear transformations and matrices.
• Discover a straightforward test for matrix invertibility.
• Investigate some beautiful and useful determinant properties.
• Learn how to work with important special vectors.
• Discover a foolproof method for calculating eigenvalues.

Syllabus :

1. Linear Equations

• Two Linear Equations in Two Unknowns
• Three Unknowns
• Gaussian Elimination
• The Full Story of Gaussian Elimination

 

2. Vector Spaces

• Vector Spaces
• Subspaces and Span
• Linear Independence
• Basis and Dimension

 

3. Properties of Matrices

• Matrix Algebra
• Inverses and Systems of Equations
• Four Fundamental Subspaces
• Adjacency Matrices

 

4. Linear Maps and Matrices

• Linear Transformations
• Properties of Linear Transformations
• 2x2 Determinants
• Determinants in Higher Dimensions

 

5. Eigenvalues and Diagonalizability

• Eigenvalues and Eigenvectors
• Characteristic Polynomial
• Diagonalizability
• PageRank and Exponentiation

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