Lectures related to Multilinear Forms: Notation & Applications

Tensor Products of Modules

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

Tensor Products and Symmetric Power

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

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Linear Algebra in Dirac Notation

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

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Independence and Basis

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

Lie Algebras and Representations

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

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Lorentz Transformations and Covariant Tensors

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Orthogonality and Projection

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

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, focusing on states, time evolution, and measurement.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Singular Vectors in Liouville CFT: Representation Theory Insights

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Coordinate Systems and Applications

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.