Linear Algebra
Delve into the abstract depths of linear algebra: vector spaces, determinants, eigenvalues, wedge products, and more.
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Course description
Linear algebra plays a crucial role in many branches of applied science and pure mathematics. This course covers the core ideas of linear algebra and provides a solid foundation for future learning. Using geometric intuition as a starting point, the course journeys into the abstract aspects of linear algebra that make it so widely applicable. By the end you'll know about vector spaces, linear transformations, determinants, eigenvalues & eigenvectors, tensor & wedge products, and much more. The course also includes applications quizzes with topics drawn from such diverse areas as image compression, cryptography, error coding, chaos theory, and probability.
Topics covered
- Bases
- Determinants
- Diagonalizable Matrices
- Eigenvalues and Eigenvectors
- Gaussian Elimination
- Gram-Schmidt Process
- Inner Products
- Inverses
- Linear Independence
- Linear Transformations
- Matrices
- Subspaces
- Tensors & Tensor Products
- Vector Spaces
Prerequisites and next steps
A basic understanding of calculus and linear equations is necessary.