## Elementary Linear Algebra 7th Edition

$u=(0,1)$, then $\langle u.u\rangle=\langle (0,1).(0,1)\rangle=-2<0$.
Let $u=(0,1)$, then $\langle u.u\rangle=\langle (0,1).(0,1)\rangle=-2<0$. This shows that the function does not satisfy the conditions of the inner product.