# Vectors and Matrices

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## Abstract

What is a vector? It is a finite list of (real) numbers: scalars or components. In a geometrical context, the components have yet another name: coordinates. In the two-dimensional Cartesian plane, for example, a vector contains two coordinates: the *x*- and *y*-coordinates. This is why the vector is often denoted by the pair (*x*, *y*). Geometrically, this can also be viewed as an arrow, leading from the origin (0, 0) to the point \((x, y)\in \mathbb {R}^2\). Here, \(\mathbb {R}\) is the real axis, \(\mathbb {R}^2\) is the Cartesian plane, and “\(\in \)” means “belongs to.”

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