Coxeter Groups: Geometric Equivalence and Positive Definite Graphs

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

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Covers matrix multiplication, properties, and inverses in linear algebra.

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.