Lectures related to Antilinear map

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Linear Algebra: Basis Change and Matrices

Explores basis change in linear algebra and the role of matrices.

Chaos Theory: Chaotic Maps and Logistic Map

Explores chaotic maps, fix points, periodic orbits, and intermittent chaos.

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Linear Algebra Basics

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Dot Product: Properties and Applications

Explores the properties and applications of the dot product in vector spaces.

Linear Applications: Properties and Examples

Explores properties of linear applications, including symmetric matrices and linearity in analysis.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.

Change of Basis: Transition Matrices

Covers change of basis, transition matrices, and matrix similarity.

Linear Maps and Linear Independence

Explores linear maps and linear independence under surjective linear maps.

Exam Q10 solution

Discusses the misconception that an injective linear map must have M strictly smaller than N.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Singular Values and Norms: Understanding Linear Maps with SVD

Explores singular value decomposition and its role in understanding linear maps.

Linear Maps: Dimension and Bases

Explores the dimension of linear maps and the construction of bases.

Linear Applications: Matrices and Properties

Explores linear applications, matrices, injectivity, surjectivity, and compositions of linear maps with examples and demonstrations.

Linear Maps and Bases: The Rank Theorem

Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.

Vector Spaces: Definitions and Applications

Introduces vector spaces, subspaces, linear maps, and evaluation maps, with examples and exercises for better comprehension.

Complex Functions: Linear and Anti-linear

Covers complex functions, linear and anti-linear functions, harmonic polynomials, rational functions, and exponential functions.

Tensor Products and Symmetric Power

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

The Regular Representation

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