Vectors and matrices

Notation:

• Vector $x\in {\mathbb{R}}^n$ and components: $x=(x_1,\dots ,x_n)$.
• Matrix $A\in {\mathbb{R}}^{m\times n}$. Entry: $a_{ij}$ in lower case.

$$A=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1n}\\ a_{21}& \dots & & \\ ⋮& & & \\ a_{m1}& \dots & & a_{mn}\end{array}\right)$$

We will also consider situations where $\mathbb{R}$ is replaced by $\mathbb{C}$.