In this chapter, some of the mathematical concepts are reviewed. This chapter also reviews some properties of vectors and matrices and introduces some of the vocabulary used in optimization theory. It also discusses the properties of the solution of a system of linear equations.

Chapter Contents:

• 1.1 Introduction
• 1.2 Vectors
• 1.3 Matrices
• 1.4 The solution of linear systems of equations
• 1.5 Derivatives
• 1.5.1 Derivative approximation
• 1.5.2 The gradient
• 1.5.3 The Jacobian
• 1.5.4 Second-order derivatives
• 1.5.5 Derivatives of vectors and matrices
• 1.6 Subspaces
• 1.7 Convergence rates
• 1.8 Functions and sets
• 1.9 Solutions of systems of nonlinear equations
• 1.10 Optimization problem definition
• References
• Problems

Inspec keywords: vectors; optimisation; matrix algebra

Other keywords: vector properties; matrix properties; mathematical concepts; optimization theory; linear equations

Subjects: Optimisation techniques; Linear algebra (numerical analysis); Optimisation; Linear algebra (numerical analysis); Numerical analysis; Optimisation techniques