When reading about the inner product for complex vector spaces, some sources say that the inner product must satisfy $\langle c\vec{u}, \vec{v}\rangle = \bar{c}\langle \vec{u}, \vec{v} \rangle $ and $\langle \vec{u}, c\vec{v}\rangle = c\langle \vec{u}, \vec{v} \rangle $ where other sources say that $\langle \vec{u}, c\vec{v}\rangle = \bar{c}\langle \vec{u}, \vec{v} \rangle $ and $\langle c\vec{u}, \vec{v}\rangle = c\langle \vec{u}, \vec{v} \rangle $. Is there a reason to use one convention over another? Is one more 'common'?
Source for the first version:
http://www.math.umd.edu/~hking/Hermitian.pdf
Source for the second version