Solution
= Solution
Positivity and $\|x\|\leq t$ give $\sigma(x)\subset[0,t]$. Hence
$$
\sigma(t1-x)\subset[0,t].
$$
The element $t1-x$ is hermitian, so its norm equals its spectral radius and is at most $t$.
= Solution
Positivity and $\|x\|\leq t$ give $\sigma(x)\subset[0,t]$. Hence
$$
\sigma(t1-x)\subset[0,t].
$$
The element $t1-x$ is hermitian, so its norm equals its spectral radius and is at most $t$.