Lectures related to Binary quadratic form

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

Quadratic Forms and Symmetric Bilinear Forms

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

Pseudo-Euclidean Spaces: Isometries and Bases

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

Quadratic Forms: Definitions, Examples MOOC: Linear Algebra (Part 3)

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

Classification of Quadratic Forms MOOC: Linear Algebra (Part 3)

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

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.

Non-Negative Definite Matrices and Covariance Matrices

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

Elliptical Distributions: Properties and Applications

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Topology of Adeles

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

Gaussian Random Vectors

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

Quadratic Forms and Hecke Operators

Explores quadratic forms, Hecke operators, eigenvalues, and compactly supported functions in matrix theory.

Hamiltonian Mechanics: Analytical Approach

Explores Hamiltonian mechanics, conservation laws, potential functions, and canonical transformations in analytical detail.

Iterative Methods for Linear Equations

Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.

Principal Axes Theorem MOOC: Linear Algebra (Part 3)

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

Quadratic Forms in IR³ MOOC: Linear Algebra (Part 3)

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

Linear Regression: General Form

Covers the design matrix, response vector, and linear vs affine regression.

Integral Representations: Quadratic Lattices and Hasse Principle

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

Optimal Control: KKT Conditions

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

Linear Quadratic Optimal Control: Analysis and Solution

Explores Linear Quadratic optimal control, analyzing cost, and presenting the solution to the FH-LQ problem.