Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Digital systems, linear algebra, introduction to formal proof / 6 / b

For a square matrix $M$, an eigenvalue–eigenvector pair is a scalar $\lambda$ and a nonzero vector $v$ satisfyingThus the linear map represented by $M$ scales this particular direction by $\lambda$. The nonzero condition excludes the zero vector, which would otherwise satisfy the displayed equation for every scalar.