Projectors and Tensor Product of Representations

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Character of Dirac and Projectors

Discusses Dirac's character and projectors in high-dimensional spaces with matrices and vectors.

Tensor Product: Bilinear Maps

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

Tensor Products of Modules

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

Projectors on Invariant Subspaces

Covers projectors on invariant subspaces in quantum physics and their applications.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Principles of Quantum Physics

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Cohomology: Cross Product

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

Reduced Density Matrices: System+Environment

Covers the concept of density matrices and the system-environment interaction.

Tensor Products and Symmetric Power

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

Decomposition Principle: Linear Algebra

Explores the decomposition principle in linear algebra, showing how a vector space can be split into two subspaces.