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Concept

Sesquilinear form

Related lectures (29)

Quadratic Forms and Symmetric Bilinear Forms

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

Weingarten Application of Regular Surfaces

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

Spectral Theorem Recap

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

Hermitian Forms: Definition and Properties

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

Bilinear Forms: Theory and Applications

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

Interpolation of Lagrange: Dualité and Coupling

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Differential Forms on Manifolds

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

Conformity and Compliancy in Geometry

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

Pseudo-Euclidean Spaces: Isometries and Bases

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

Hermitian Operators and Spectral Theorem

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

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

Harmonic Oscillator: Damped Regimes

Explores the analysis of a harmonic oscillator under different damping regimes, focusing on strong and critical damping.

Hilbert Spaces: Definition and Properties

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Finite Element Method: 2D Analysis Log in to Mediaspace to watch this video

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

Finite Elements Method: Application Example 2D Log in to Mediaspace to watch this video

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

Lax-Milgram: Variational Problems and Riesz's Theorem Log in to Mediaspace to watch this video

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

Orthogonality and Inequalities Log in to Mediaspace to watch this video

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