## Elementary Linear Algebra 7th Edition

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