Concept

Quadratic function

Related lectures (31)

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Mild Dissipative Surface Dynamics

Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.

Optimization Methods

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Quadratic Surfaces in 3D Space

Explores quadratic surfaces in 3D space, discussing hyperboloids and their Cartesian equations, emphasizing the importance of reference frames.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Optimality Conditions: Quadratic Functions

Covers the formulation of quadratic functions and optimality conditions for finding the global optimum.

Response Surfaces I: LoF and Plans

Explores lack of fit concept and experimental designs for second-degree functions.

Algebra: Quadratic Trinomial

Explores quadratic trinomials, absolute values, Vieta's formulas, and graphical representation of equations.

Symmetric Matrices and Quadratic Forms

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

Quadratic Equation: Programming Solutions

Covers the programming of a script to calculate the solutions of quadratic equations.

Polynomials with Real Coefficients

Explores polynomials with real coefficients, complex roots, and sequences' properties.

Strong Convexity and Convergence Rates

Explores strong convexity's role in faster convergence rates for optimization algorithms.

Decomposition: Simple and Quadratic Factors

Explores the decomposition of a function into simple and quadratic factors.

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Complex Numbers and 2x2 Matrices

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.

Mechanical Energy Conservation

Explores mechanical energy conservation, potential and kinetic energy relationship, laws of motion, and harmonic oscillator.

Symmetric Matrices and Quadratic Forms

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

Equidistribution of CM Points

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

Polynomial Optimization: Theory and Applications

Explores polynomial optimization, emphasizing sum-of-squares polynomials and their applications, including monomial representation and theorem proofs.

Completing the Square in Quadratic Polynomials

Demonstrates completing the square in quadratic polynomials for factorization simplification.