The derivation and analysis of the methods for solving linear systems of equations considered in the following are based on the fundamentals presented in this chapter. Here, we always consider mappings between real or complex linear spaces, which are often also referred to as vector spaces over \({\mathbb{R}}\) or \({\mathbb{C}}\) , respectively. Such linear spaces, for example \({\mathbb{R}}^n\) or \({\mathbb{C}}^n\) , are non-empty sets whose elements can be combined by addition and multiplied by scalars \(\lambda \in {\mathbb{R}}\) or \({\mathbb{C}}\) , satisfying the vector space axioms. These axioms merely guarantee that addition, subtraction, and multiplication can be performed as usual. In addition to various vector and matrix norms, the scalar product as well as the important concepts of eigenvalue, eigenvector, and spectral radius are introduced. Of central importance with regard to the investigation of the convergence of some iterative methods is also the Banach fixed point theorem presented in this section.