Concept

Tensor product of modules

Related lectures (32)

Tensor Products of Modules

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

Tensor Product: Bilinear Maps

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Linear Algebra in Dirac Notation

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.

Lie Algebras and Representations

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Projectors and Tensor Product of Representations

Explores projectors and tensor product of representations, covering their applications and properties.

Tensor Spaces and Unitary Representations

Explores tensor spaces, unitary representations, and prime factorization in mathematical presentations.

Group Homomorphisms

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

Rings and Modules: Color Codes and Homological Algebra

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Signature Kernels: Universal Feature Sets for Data Science

Explores signature kernels, feature maps, tensor algebras, and their applications in data science and machine learning.

Quantum Physics I: Entanglement and Commutation Relations

Explores entanglement and commutation relations in quantum physics, focusing on Clebsch-Gordan coefficients and tensor-product basis.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Tensor Products and Symmetric Power

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

States of Composite Systems

Covers the states of composite systems in Hilbert space, including operators, observables, tensor products, eigenvalues, and partial measurements.

Linear Quantum Calculus in Dirac Notation

Covers linear algebra in Dirac notation, emphasizing the scalar product and density product in quantum computations.

Ring Structure: Polynomials and Coefficients

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Coulomb Gas and Spin Chain: Quantum Group Applications

Explores the relationship between Coulomb gas models and spin chains in quantum groups.

Thermodynamics of Continuous Media

Covers historical thermodynamics, continuity equations, state functions, and Cartesian products in scalar and vectorial forms.