Quadratic Forms and Symmetries

Related lectures (31)

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

Explores examples of algebraic quotients using invariance maps and discriminant.

Explores the theory of Hermitian spaces and their applications in quadratic forms and codimension 1 spaces.

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

Covers elliptical distributions, including properties, applications, and risk management implications.

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

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