Group Actions: Examples

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Related lectures (27)

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Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Linear Applications and Span

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Linear Algebra Basics

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Linear Transformations: Matrices and Bases

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

The Regular Representation

Introduces the regular representation, a key tool for studying group actions on varieties.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.