Lectures related to Multilinear Forms: Definitions and Properties

Determinants: Alternate Forms and Symmetrization

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Multilinear Forms: Alternating and Symmetric

Covers alternating and symmetric multilinear forms in vector spaces over a field.

Tensor Products and Symmetric Power

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

Permutations and Signature

Explores permutations, signature, and alternating multilinear forms in vectors.

Linear Algebra: Multilinear Forms

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Linear Algebra: Multilinear Forms

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Determinants: Theory and Applications

Covers the theory of determinants and their applications in linear algebra.

Linear Algebra: Multilinear Forms

Explores multilinear forms in linear algebra, emphasizing their role in vector space transformations.

Linear Algebra: Multilinear Forms

Introduces multilinear forms in linear algebra, emphasizing clarity and logic in presentation.

Multilinear Forms: Notation & Applications

Covers multilinear forms in n variables over a k-vector space, emphasizing notation and applications.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Bilinear Forms: Theory and Applications

Covers the theory and applications of bilinear forms in various mathematical contexts.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.

Linear Applications: Properties and Examples

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

Linear Algebra: Multilinear Groin and Determinants

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

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Symmetric Matrices: Diagonalization

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