Inner product of complex numbers

[Baron]

My attached class notes says the inner product of two complex vectors w and z with n enteries is

<w,z> = summation from i = 1 to n of the complex conjugate of wi*zi

Is this wrong? I was checking online and it says the inner product of two complex vectors is the summation from i = 1 to n of wi*complex conjugate of zi

Please see the attachment for the typed notes and clarity.

 

[Ishuda]

My attached class notes says the inner product of two complex vectors w and z with n enteries is

<w,z> = summation from i = 1 to n of the complex conjugate of wi*zi

Is this wrong? I was checking online and it says the inner product of two complex vectors is the summation from i = 1 to n of wi*complex conjugate of zi

Please see the attachment for the typed notes and clarity.

Strange but true:
From a formal definition standpoint, either one will work although there are differences (linearity in the first as opposed to the second argument, etc.). This is another of those differences one finds between mathematicians and, say, engineers.
Mathematician: <w, z> = \(\displaystyle \Sigma_j w_j^* z_j\); w* = Rl(w) - i Im(w), z = Rl(w) + i Im(z), i² = -1.
Engineer: <w, z> = \(\displaystyle \Sigma_i w_i z_i^*\); w = Rl(w) + j Im(w), z* = Rl(w) - j Im(z), j² = -1.

It depends on the context.