This question already has an answer here:
For $V_n$ where $x=(x_1, x_2, \ldots, x_n)$ and $y=(y_1,y_2,\ldots,y_n)$, the dot product is defined by $x_1y_1+x_2y_2+ \cdots+x_ny_n$.
In Apostol's calculs vol 2
It says that if $x=(x_1,x_2)$ and $y=(y_1,y_2)$ are any two vectors in $V_2$, define $(x \cdot y)$ by the formula
$(x \cdot y)= 2x_1y_1+x_1y_2+x_2y_1+x_2y_2$
Why is that?
Is there difference between dot and inner product?
I thought that following the dot product, $(x \cdot y)$ should be $x_1y_1+x_2y_2$.