Eigenvalues

Dive into a comprehensive exploration of eigenvalues and matrix operations through a series of engaging lectures totaling 7 hours. Learn to diagonalize 2x2 and 3x3 matrices, understand complex eigenvalues, and explore the fascinating connections between matrices and popular culture references like Legend of Zelda and Pokémon. Discover advanced concepts such as matrix exponentials, systems of differential equations, and Jordan Canonical Form. Investigate unique applications including matrix limits, Markov chains, and even matrix factorials. Engage with creative approaches to understanding matrix operations, from imaginary powers to matrix square roots, all while developing a deep understanding of these fundamental mathematical concepts.

Syllabus

Diagonalize 2x2 matrix.
Diagonalize 3x3 matrix.
Diagonalization and Legend of Zelda.
Not diagonalizable.
Derivative in a box.
Matrix of a matrix.
Matrix with respect to a basis.
Complex eigenvalues.
Pokémon battle.
Fibonacci sequence.
Square root of a matrix.
e to a matrix.
Matrix to a matrix.
Matrix exponential properties.
System of differential equations.
Cos of matrix.
Arctan of a Matrix.
A^2020.
Limit of a matrix.
Matrix Limits and Markov Chains.
Matrix Limit Gone Wrong.
Jordan Canonical Form.
FAST eigenvalues.
Diagonalize 4x4 Matrix.
matrix factorial.
i^i with matrices.
Imaginary power of a matrix.
Square root of matrix #shorts.
imaginary root of matrix.
matrix choose a matrix.