Hello,

I would appreciate your help on the following problem.

A rule being used to define the mathematics of a vector space is

$\displaystyle

<\vec{u},\vec{v}>=u_{1}v_{2}+u_{2}v_{1}

$

Determine and state which axiom fails.

I tried the four axioms (symmetry, additive, homogeneity, and positive definite), but none seems to fail. Am I missing anything?

Thank you in advance!