Lectures related to Degenerate bilinear form

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.

Quadratic Forms and Symmetric Bilinear Forms

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

Differential Forms on Manifolds

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

Pseudo-Euclidean Spaces: Isometries and Bases

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

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.

Spectral Theorem Recap

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

Geometric Properties of Dot Product

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Lax-Milgram: Variational Problems and Riesz's Theorem

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

Simple Lie Algebras: Classification and Properties

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

Abstract Variational Problems

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

Scalar Product: Algebraic Properties

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

Orthogonality and Inequalities

Explores symmetrical bilinear forms, the Pythagorean theorem, inequalities, and orthogonal matrices.

Bilinear Forms

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

Linear Algebra: Multilinear Forms

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

Quadratic Lattices: Properties and Equidistribution

Covers non-degenerate quadratic lattices, local representability, equidistribution, and the Siegel theorem.

Lie Algebra: Vector Space and Multiplication Law

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

Tensor Products and Symmetric Power

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