Lectures related to Quadratic Forms and Symmetric Bilinear Forms

Pseudo-Euclidean Spaces: Isometries and Bases

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

Linear Algebra: Quadratic Forms and Matrix Diagonalization

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

Bilinear Forms: Theory and Applications

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

Differential Forms on Manifolds

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

Scalar Product and Euclidean Spaces

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Bilinear Forms

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

Hermitian Forms: Definition and Properties

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

Spectral Theorem Recap

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

Interpolation of Lagrange: Dualité and Coupling

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

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Conformity and Compliancy in Geometry

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Weingarten Application of Regular Surfaces

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

Linear Algebra: Multilinear Forms

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

Sylvester's Inertia Theorem

Explores Sylvester's Inertia Theorem, relating eigenvalues to diagonal entries in symmetric matrices.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Norm, Dot Product, Orthogonality

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

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.