Lectures related to Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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

Quadratic Forms: Definitions, Examples

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

Quadratic Forms and Symmetric Matrices

Explores examples of algebraic quotients using invariance maps and discriminant.

Principal Axes Theorem

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

Quadratic Forms in IR³

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

Sylvester's Inertia Theorem

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

Quadratic Forms and Symmetric Bilinear Forms

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

Non-Negative Definite Matrices and Covariance Matrices

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

Linear Algebra: Quadratic Forms and Matrix Diagonalization

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

Optimal Control: KKT Conditions

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

Pseudo-Euclidean Spaces: Isometries and Bases

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

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

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

Stationary Points and Saddle Points

Explores stationary points, saddle points, symmetric matrices, and orthogonal properties in optimization.

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.

Spectral Theorem Recap

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

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Hermitian Spaces: Theory and Applications

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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