Lectures related to Quadratic Forms and Symmetric Matrices

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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

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

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

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

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

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

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

Covers non-negative definite matrices, covariance matrices, and Principal Component Analysis for optimal dimension reduction.

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

Explores optimal control and KKT conditions for non-linear optimization with constraints.

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

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

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

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

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Explores integral representations, quadratic lattices, and the Hasse Principle.

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