I am trying to apply Givens rotation to a matrix, I could do it when the matrix had real values. For example, for this matrix:
$A=\begin{bmatrix}3&5\\4&1\end{bmatrix}$
I can simply calculate $sin$ and $cos$ like this:
$r=\sqrt{3^2+4^2}=5$
$cos=3/r=0.6, sin=4/r=0.8$
But when the values are complex numbers, I have a problem in determining which value of $r$ to select. For example:
$A=\begin{bmatrix}3+1.5i&5-7i\\4-2i&1+3i\end{bmatrix}$
$r=((3+1.5i)^2+(4-2i)^2)^{0.5}=4.403-0.795i$ or $-4.403+0.795i$
So the question is, Which value of $r$ should I select? What is the criteria?
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@BrianBorchers Unfortunately no, it may be a close question, but there is no satisfactory answer. – AbdelAziz AbdelLatef Mar 26 '20 at 21:41
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The second answer to that question gives fairly explicit instructions on how to do the complex Givens rotation. – Brian Borchers Mar 26 '20 at 21:48
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@BrianBorchers I will inspect it and see. – AbdelAziz AbdelLatef Mar 26 '20 at 21:53
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@BrianBorchers I think you are right, it actually solves it. – AbdelAziz AbdelLatef Mar 26 '20 at 22:20