I am studying inner product space.
One thing thing that I am trying to understand is, "How you define inner product?"
For example For $\mathbb R^3$, if $ x=(x_1, x_2, x_3),\, y=(y_1,y_2,y_3)$, what is $(x\cdot y)$ ? is is just $x_1y_1+x_2y_2+x_3y_3$ ?
Or I have a complex number such that (1+2i, 3+5i) what would be the inner product of it