Complex dot product doesn't conjugate

Inner product on ℂ is supposed to be sesquilinear – it should conjugate one of the two vectors before multiplying them. Source.

const I = math.complex(0,1)
math.dot( [1,0], [I,0] ) // I
math.dot( [I,0], [1,0] ) // I

The current dot product clearly doesn’t conjugate neither one of the vectors. This is also true of multiply(Vector, Vector) which apparently has a different implementation than dot.

While the Wikipedia article I linked uses the convention <v, w> = vᵀ w̅ (inner product is linear in the first argument and antilinear in the second argument), the opposite convention <v, w> = v⁺ w = v̅ ᵀ w is used as often, if not more. (For example in quantum mechanics, the first argument is exclusively antilinear.)

[josdejong]

Thanks Michal!

1. Since the behavior changes (though you could maybe pitch it as a bug fix) I think it’s best to make it a major, breaking change. Which is no problem at all, it’s just changing a different number in the version number 😃
2. I’m not an expert on this subject, so I think it would be best to follow what other math applications do (Matlab, Mathematica, Python numpy, …). What do you think?

[m93a]

Hey Jos, Yes, I agree that in mathjs it makes sense to offer just one solution which does conjugate. I also confirm that the PR is ready to be merged 😃