I'm writing a linear algebra exam next week and it's come to my attention that the prof that designed the test uses a different convention for complex inner product than the one my prof taught me.
I learned that the complex inner product is linear in the second argument and conjugate linear in the first, ie: $$i \langle v, w\rangle = \langle v, iw\rangle = \langle -iv, w\rangle$$
The prof's version is linear in the first argument: $$i\langle v, w\rangle = \langle iv, w\rangle = \langle v, -iw\rangle$$
I understand it's just a matter of convention and that two vectors that are orthogonal under one convention are also orthogonal in the other.
But for the purposes of the exam, does this have any affect on formulae?
For example, projection of $v$ onto $w$ is $\langle v, w\rangle w/\langle w, w\rangle$ the way I learned it. If I'm using the prof's version do I need to flip it to get the answer they're expecting?