Could someone give me some hint about a possible method to find the function $f$ which solve this equation: $$f(H^2)=\alpha f(H)$$ where $\alpha$ a constant with $\alpha \in C$ and: $$H=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$$ a matrix with complex elements?
Matrix functional equation
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matrices
functional-equations
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0$f$ give a matrix or a complex number? – 2012-06-28
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0$f$ should give a matrix – 2012-06-28
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0You certainly need to put some conditions on $f$, unless you are happy with the solution $f=0$. – 2012-06-29
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0@Martin Argerami: I agree. Obviously the trivial solution $f=0$ has to be rejected. – 2012-07-02