could someone help me with this simple problem. As always with homework, hints are specially welcome.
Let $v=(v_1,v_2)$ be a two-dimensional unit vector with complex coefficients. If $|v_1| and $|v_2| then $|v_1|+|v_2|\geq \frac{1}{a}$.
could someone help me with this simple problem. As always with homework, hints are specially welcome.
Let $v=(v_1,v_2)$ be a two-dimensional unit vector with complex coefficients. If $|v_1| and $|v_2| then $|v_1|+|v_2|\geq \frac{1}{a}$.
I think I got it.
\begin{equation} |v_1|+|v_2|\geq \frac{|v_1|}{a}|v_1|+\frac{|v_2|}{a}|v_2|\geq \frac{|v_1|^2+|v_2|^2}{a}=\frac{1}{a} \end{equation}