 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-106/5/4/solution

Positivity and

∥ x ∥ \leq t

give

σ (x) \subset [0, t]

. Hence

σ (t 1 - x) \subset [0, t] .

The element

t 1 - x

is hermitian, so its norm equals its spectral radius and is at most

t

 New to topics? Read the docs here!