Euclidean vector space/Linear mapping/Orthogonal diagonalizable/Eigenvalues and norm/Exercise

Let ${}V$ denote a Euclidean vector space, and let

$\varphi \colon V\longrightarrow V$

be a linear mapping such that there exists an orthogonal basis of ${}V$ consisting of eigenvectors of ${}\varphi$. Show that

${}\Vert {\varphi }\Vert ={\max {\left(\vert {\lambda }\vert ,\lambda {\text{ is eigenvalue of }}\varphi \right)}}\,$

holds.

Create a solution