Lectures related to Bilinear map

Bilinear Forms: Theory and Applications

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

Conformity and Compliancy in Geometry

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

Differential Forms on Manifolds

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

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Tensor Product: Bilinear Maps

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Abstract Variational Problems

Covers abstract variational problems in Hilbert spaces, focusing on boundedness, continuity, and coercivity.

Quadratic Forms and Symmetric Bilinear Forms

Explores quadratic forms, symmetric bilinear forms, and their properties.

Geometric Properties of Dot Product

Covers the geometric properties of the dot product and its algebraic aspects.

Tensor Products and Symmetric Power

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

Simple Lie Algebras: Classification and Properties

Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Finite Element Method: 2D Analysis

Explores the finite element method for 2D analysis, covering assembly, matrices, sources, and convergence criteria of quadrangular elements.

Finite Elements Method: Application Example 2D

Explores the application of finite elements method in 2D temperature distribution on a square plate.

Scalar Product: Algebraic Properties

Explores the algebraic properties of the scalar product and their geometric implications.

Spectral Theorem Recap

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

Lax-Milgram: Variational Problems and Riesz's Theorem

Explores the Lax-Milgram theorem, variational problems, and Riesz's representation theorem in linear elliptic problems.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Lie Algebra: Vector Space and Multiplication Law

Covers Lie Algebra, focusing on vector space and multiplication law.

Lie Algebra: Bilinearity and Jacobi Identity

Covers Lie algebra, bilinearity, Jacobi identity, and Ado's theorem.

Norm, Dot Product, Orthogonality

Explores norm, dot product, and orthogonality in vector spaces, including properties and inequalities.