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I want to solve following minimization problem using lagrange multipliers... i have problem computing derivatives w.r.t complex matrx K .. can anybody do it?

$$\min_K \quad trace(KRK^{H}) \qquad \text{s.t. } KH=I $$

Thanks

alam
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    What is $H$? What does $H^H$ stands for? Since you have a constraint $KH = I$, then the objective is reduced to $H^H$. But is $H^H$ is scalar or a matrix? – Guangliang Apr 14 '17 at 18:39
  • I have rephrased the question,,,all of these are matrices, $K^H$ is hermitian i.e, conjugate transpose of $K$ and $H$ can be any matrix. – alam Apr 15 '17 at 04:42
  • But still, the expression $KRK^H$ is a matrix. What do you mean by minimizing a matrix? – Guangliang Apr 15 '17 at 13:11
  • Assume we want to minimise the trace of the matrix.. – alam Apr 16 '17 at 17:15

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