I need to minimize the Frobenius norm of (A-k*B) by finding appropriate value for k.
In this question A and B are m*n known matrices.
We know that (norm(A-kB))^2=trace((A-kB)(A-k*B)')
When A and B are real numbered matrices, the question can be easily solved by minimizing the following equation(by taking derivative regarding to k) min(Trace[(A-kB)(A-kB)']) ' denotes complex conjugate operator.
In this situation k is the sole variable of the question.
However, when A and B are complex numbered matrices, k has to be complex. In this situation, in the second parentheses, after applying ' operator k changes to k'. Now both of k and k' are the unknown variables of the problem. Doing the above minimization gives only k+k' not k. It would be appreciated if you could help me on solving this question.