Algebra

Related lectures (25)

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Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

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

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

Covers principal ideals, ring homomorphisms, and more in commutative rings and fields.