I have two arrays $a$ and $b$ containing complex values. Now I one of my target operations is the following: $$||a-b||$$ The result should be a single real number. Now I am a bit confused how to apply the norm here: Should I rather calculate first the norm of each value in the array, and then apply the formula above: $$a[i] = \sqrt(a[i].real^2+a[i].imag^2)$$ $$||a[i]-b[i]||$$ or should I first subtract the values, and then apply the formula: $$tmp = a[i]-b[i]$$ $$||tmp|| = \left(\sum \sqrt(tmp.real^2 + tmp.imag^2)^n\right)^{\frac{1}{n}}$$? What is intended by the operation shown above?
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$\begingroup$For any complex vector $$\|c\|=\sqrt{\langle c,c\rangle}=\sqrt{\sum_{i=1}^nc_i\overline{c}_i}.$$
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