Learn the mathematics behind linear algebra and link it to matrix software development. Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets.

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Students appreciate our unique approach to teaching linear algebra because:

- It’s visual.

- It connects hand calculations, mathematical abstractions, and computer programming.

- It illustrates the development of mathematical theory.

- It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

What you'll learn:

- Connections between linear transformations, matrices, and systems of linear equations

- Partitioned matrices and characteristics of special matrices

- Algorithms for matrix computations and solving systems of equations

- Vector spaces, subspaces, and characterizations of linear independence

- Orthogonality, linear least-squares, eigenvalues and eigenvectors

Course Syllabus

Week 0 Get ready, set, go!

Week 1 Vectors in Linear Algebra

Week 2 Linear Transformations and Matrices

Week 3 Matrix-Vector Operations

Week 4 From Matrix-Vector Multiplication to Matrix-Matrix Multiplication

Exam 1

Week 5 Matrix-Matrix Multiplication

Week 6 Gaussian Elimination

Week 7 More Gaussian Elimination and Matrix Inversion

Week 8 More on Matrix Inversion

Exam 2

Week 9 Vector Spaces

Week 10 Vector Spaces, Orthogonality, and Linear Least Squares

Week 11 Orthogonal Projection and Low Rank Approximation

Week 12 Eigenvalues and Eigenvectors

Final