MATLAB: Multiplication of complex matrices

complex matrix multiplication

I have noticed that when I multiply 2 matrices with complex elements A*B, Matlab takes the complex conjugate of matrix B and multiplies A to conj(B).
For example I have a complex vector a = [2+0.3i, 6+0.2i], so the multiplication a*(a') gives 40.13 which is not correct. However, when I want to calculate square of the norm of vector 'a' norm_square = a*conj(a)' I get complex number which is a sum of squares of the vector components.
My question is: is it a bug or I just dont get the way matlab works with complex numbers?

Best Answer

There are two different operators:
' is the complex conjugate transpose
.' is the straight transpose (no complex conjugate), notice the dot
Use the operator that is appropriate for your application. If you only want the transpose with no conjugation, then use the dot version .'
Side Note: Related to this, the dot( ) function effectively uses the ' operation internally ... i.e., it does a complex conjugate of the first argument.
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