Concept

Definite quadratic form

Related lectures (31)

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Bilinear Forms: Theory and Applications

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

Quadratic Forms and Symmetric Bilinear Forms

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

Symmetric Matrices and Quadratic Forms

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

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.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Linear Quadratic (LQ) Optimal Control: Proof of Theorem

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Pseudo-Euclidean Spaces: Isometries and Bases

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

Classification of Quadratic Forms

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

Symmetric Matrices and Quadratic Forms

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

Weingarten Application of Regular Surfaces

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

Linear Models: Ridge, OLS and LASSO

Covers linear models like Ridge, OLS, and LASSO, explaining singular values and regression analysis.

Lorentz-Minkowski Spacetime

Covers Lorentz-Minkowski spacetime, speed of light interpretation, isometries, and special relativity principles.

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Quadratic Forms in IR³

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.

Spectral Theorem Recap

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

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

Compact Manifolds Classification

Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.