Representation Theory: Algebras and Homomorphisms

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Covers matrix equations as linear combinations, vector spaces, and geometric interpretations.

Explores the decomposition of the circle of the coordinate ring of a G variety into a direct sum of simple submodules.

Explores area determination, linear applications, matrix operations, and vector spaces.

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Covers advanced Python topics like numpy operations, scipy linear algebra, and matplotlib for creating figures.

Explores natural transformations in algebra, defining functors and isomorphisms.

Introduces orthogonal sets and bases, discussing their properties and linear independence.

Explores linear algebra concepts through examples and theorems, focusing on matrices and their operations.

Covers the definition and examples of vector spaces, including subspaces and linear transformations.

Explores the properties and applications of the dot product in vector spaces.

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

Explores Sylvester's Theorem and the importance of orthogonal bases in linear algebra.

Covers kernels and images of linear transformations between vector spaces.

Explores the properties and applications of orthogonal matrices in linear algebra, focusing on orthogonality and projections.

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

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