Adding, not disagreeing, but at some point, those abstract concepts like dot products become concrete on their own when you get into things like SIMD programming.
Yeah, but to arrive at that point, you'd have to have understood dot products already.
It's one thing to take two float arrays, multiply them componentwise and sum the results. It's another thing to understand why this operation constitutes the dot product in R^n vector spaces.
You also have to understand that a^T b is a popular way of writing the dot product. <a,b> is for dumb high schoolers.
Then there is the fun part in German that the dot product and inner product are both called Skalarprodukt. There are many inner products of which the dot product is only one.
It's one thing to take two float arrays, multiply them componentwise and sum the results. It's another thing to understand why this operation constitutes the dot product in R^n vector spaces.