Mastering Linear Algebra: An Introduction with Applications

Overview

Take your math skills to a new level with linear algebra, which is used in everything from computer graphics to quantum mechanics. “Mastering Linear Algebra: An Introduction with Applications” comprises 24 half-hour lectures that introduce fundamental concepts and practical applications in an accessible manner.

Course Instructor

This course is taught by award-winning Professor Francis Su of Harvey Mudd College, who guides you through traditional topics of a first-semester college course in linear algebra.

Video Lessons

• Linear Algebra: Powerful Transformations
  • Duration: 28 min
  • Description: Explore the core idea of linear transformations and their significance in algebra.

2. Vectors: Describing Space and Motion
   • Duration: 27 min
   • Description: Understand vectors as foundational elements in linear algebra and their applications.

• Linear Geometry: Dots and Crosses
  • Duration: 28 min
  • Description: Learn about dot products and cross products, fundamental operations in vector calculus.

• Matrix Operations
  • Duration: 31 min
  • Description: Discover matrix notation and arithmetic through practical examples in coding and error detection.

5. Linear Transformations
   • Duration: 28 min
   • Description: Investigate linear transformations and their applications in computer graphics.

• Systems of Linear Equations
  • Duration: 28 min
  • Description: Study methods for solving systems of linear equations, including Gaussian elimination.

7. Reduced Row Echelon Form
   • Duration: 28 min
   • Description: Learn to use row operations to achieve reduced row echelon form for solving equations.

8. Span and Linear Dependence
   • Duration: 31 min
   • Description: Understand the concepts of span and linear dependence in vector spaces.

• Subspaces: Special Subsets to Look For
  • Duration: 29 min
  • Description: Delve into special subsets of matrices, like null space and row space.

10. Bases: Basic Building Blocks
    • Duration: 29 min
    • Description: Explore the concept of the basis of a vector space and its applications in data compression.

11. Invertible Matrices: Undoing What You Did
    • Duration: 30 min
    • Description: Understand invertible matrices and their significance in solving linear transformations.

12. The Invertible Matrix Theorem
    • Duration: 34 min
    • Description: Discover the properties of invertible matrices and their implications.

• Determinants: Numbers That Say a Lot
  • Duration: 30 min
  • Description: Study determinants and their usefulness in understanding mathematical transformations.

14. Eigenstuff: Revealing Hidden Structure
    • Duration: 27 min
    • Description: Explore the concepts of eigenvalues and eigenvectors in detail.

15. Eigenvectors and Eigenvalues: Geometry
    • Duration: 29 min
    • Description: Analyze eigenvectors’ geometric properties and their applications in linear transformations.

16. Diagonalizability
    • Duration: 32 min
    • Description: Learn under what conditions a matrix can be diagonalized.

17. Population Dynamics: Foxes and Rabbits
    • Duration: 30 min
    • Description: Apply linear algebra to model population dynamics using differential equations.

18. Differential Equations: New Applications
    • Duration: 33 min
    • Description: Discover how linear algebra integrates into the solutions of differential equations.

19. Orthogonality: Squaring Things Up
    • Duration: 31 min
    • Description: Investigate the concept of orthogonality and its applications in linear algebra.

20. Markov Chains: Hopping Around
    • Duration: 33 min
    • Description: Learn about Markov chains and their applications in probability and statistics.

• Multivariable Calculus: Derivative Matrix
  • Duration: 31 min
  • Description: Explore the connections between linear algebra and multivariable calculus.

• Multilinear Regression: Least Squares
  • Duration: 28 min
  • Description: Understand how linear regression analyzes data and relationships among variables.

23. Singular Value Decomposition: So Cool
    • Duration: 32 min
    • Description: Study singular value decomposition and its applications in data analysis.

24. General Vector Spaces: More to Explore
    • Duration: 34 min
    • Description: Conclude with an exploration of vector spaces beyond the real numbers.