Coxeter Groups: Simple Roots and Reflections

Related lectures (22)

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Explains linear independence, basis, and matrix rank with examples and exercises.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Explores linear independence in vector spaces and the concept of bases.

Covers linear independence, bases of vectors, and solving systems using matrices.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Offers a quick review of key linear algebra concepts essential for further topics.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.