Multilinear Forms: Definitions and Properties

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Bilinear Forms

Covers bilinear forms in vector spaces, their properties, orthogonality, and equivalence conditions.

Tucker Decomposition: Multilinear rank and applications in data compression

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Tensors: Motivations and Introduction

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Hermitian Forms: Definition and Properties

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

Tensor Products of Modules

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

Representations of SU(2): Symmetries and Transformations

Covers the representations of SU(2) and their transformations in quantum mechanics.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.