Lectures related to Eigenvalues of Coxeter Elements

Coxeter groups: reflections, rotations

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Coxeter Groups: Elements, Numbers, and Planes

Explores Coxeter elements, numbers, and planes in Coxeter groups with illustrative examples.

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

Coxeter Groups: Geometric Equivalence and Positive Definite Graphs

Explores the geometric equivalence of Coxeter groups with the same graph and positive definite matrices.

Coxeter Groups: Reflections and Fundamental Regions

Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.

Geometric Transformations in R2 and R3: Visualizations and Rotations

Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.

Coxeter Groups: Classification Theorem & Order of F_4

Explores the classification theorem for Coxeter groups and the order of F_4.

Eigenvalues and Fibonacci Sequence

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Matrix Transpose: Properties and Applications

Explores the properties and applications of matrix transpose, including rotations and inverse matrices.

Orbital Angular Momentum

Explores orbital angular momentum in quantum mechanics, including rotation operators and eigenvalues.

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Rotations: Angular Momentum

Covers angular momentum in rotations, including preservation of angles and vector products.

Geometric Transformations Compositions

Covers the composition of geometric transformations in 2D, focusing on rotations and reflections to achieve specific results.

Coxeter groups: classification and crystallographic construction

Covers the classification of Coxeter groups, crystallographic construction, and Coxeter elements.

Symmetries in Mechanics and Wave Equations

Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.

Coxeter Groups: Classification and Exceptional Construction

Explores the classification and construction of Coxeter groups, focusing on exceptional cases and the method of inductive construction.

Eigenvalues and Similar Matrices

Introduces eigenvalues, eigenvectors, and similar matrices, emphasizing diagonalization and geometric interpretations.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.