Multilinear Forms: Definitions and Properties

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (34)

Linear Algebra: Multilinear Groin and Determinants Log in to Mediaspace to watch this video

Explores multilinear groin and determinants, including the Sarrus rule and proof by induction.

Differentiability: Partial Derivatives and Hessiennes Log in to Mediaspace to watch this video

Explains partial derivatives, Hessienne matrix, and their properties.

Symmetric Matrices: Diagonalization Log in to Mediaspace to watch this video

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Bilinear Forms Log in to Mediaspace to watch this video

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

Tucker Decomposition: Multilinear rank and applications in data compression Log in to Mediaspace to watch this video

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

Tensors: Motivations and Introduction Log in to Mediaspace to watch this video

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

Distributions and Derivatives Log in to Mediaspace to watch this video

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

Tensor Products of Modules Log in to Mediaspace to watch this video

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

Matrix Diagonalization: Spectral Theorem Log in to Mediaspace to watch this video

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

What is a (sub)manifold Log in to Mediaspace to watch this video

Introduces the concept of a submanifold in a linear space, defining it as a set smoothly embedded in the space.

Linear Algebra: Applications and Bases Log in to Mediaspace to watch this video

Explores unique solutions, linear dependence, canonical bases, and linear maps in linear algebra.

Systems: Properties and Behavior Log in to Mediaspace to watch this video

Covers the fundamental properties of systems in discrete and continuous time domains.

Linear Applications: Basis and Independence Log in to Mediaspace to watch this video

Covers linear independence, bases of vectors, and solving systems using matrices.

Steinitz Lemma and Cycles Log in to Mediaspace to watch this video

Explores the Steinitz Lemma and the concept of cycles in linear algebra.

Page 2 of 2