Diagonalization
Explore the fundamental concepts of linear algebra in this comprehensive 7-hour course on diagonalization. Learn about eigenvalues and eigenvectors, their relationship to linear independence, and how to diagonalize 2x2 matrices. Discover the geometric interpretation of eigenvectors and delve into topics such as pseudo diagonalization, diagonalizability, and the ultimate diagonalization test. Investigate non-diagonalizable matrices, direct sums, and the square root of a matrix. Apply diagonalization techniques to solve systems of differential equations and explore matrix limits in the context of Markov chains. Master advanced topics like the Cayley-Hamilton Theorem and simultaneous diagonalization, while also encountering interesting applications and examples, including a connection to the Legend of Zelda.