Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof / 6 / a

An eigenvalue and eigenvector pair $(\lambda ,v)$ for a square matrix $A$ satisfiesThe scalar $\lambda$ and the coordinates of $v$ belong to the chosen field, usually $\mathbb{R}$ or $\mathbb{C}$. The nonzero condition is essential: the zero vector satisfies the equation for every $\lambda$ and therefore cannot define an eigenvalue.