Algebra of Matrices: Properties and Fields

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Related lectures (31)

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Endomorphisms: Matrix Equivalence

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Push-out: Categorical Perspective on Quotients

Explores the concept of push-out in group homomorphisms.

Group Homomorphisms

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Chinese Remainder Theorem: Euclidean Domains

Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.

Algebras and Field Extensions

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Group Homomorphisms

Explores group homomorphisms, Euler's phi function, and group products.