Eigenvectors belonging to distinct eigenvalues are <linearly independent vectors>[linearly independent]. With $n$ distinct eigenvalues there are $n$ eigenvectors forming a <basis>, and the matrix is <diagonalizable matrix>[diagonalizable]. In this eigenbasis, the <Rayleigh quotient> is a weighted average of the eigenvalues, so it is maximized by choosing $\mathbf v$ in the eigenspace of the largest eigenvalue.

Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 1 / 7B / a / iii / Solution

 Solution (source code)