Linear Algebra Done Right · Problem 7A.23

Operators on Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · normal-operators

Problem

Suppose

T

is a normal operator on

V

. Suppose also that

v, w \in V

satisfy the equations

\|v\| = \|w\| = 2, \quad Tv = 3v, \quad Tw = 4w.

Show that

\|T(v + w)\| = 10