Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof (resit) / 5 / a

A scalar $\lambda$ is an eigenvalue of an $n\times n$ matrix $P$ if there is a nonzero vector $\mathbf{v}$ such thatAny such vector is an eigenvector corresponding to $\lambda$. The requirement that an eigenvector be nonzero is essential: the zero vector would satisfy the equation for every scalar and would convey no information.