Does 2D dot product, with negative second member has a special name?

Question

We have two vectors: $a, b \in \mathbb{R}^2$

The dot product is: $a_x * b_x + a_y * b_y$

But I see this formula, on many papers/articles: $a_x * b_x - a_y * b_y$

What is this formula called?

Answer 1

The closest thing I can think of is this:

A real inner product space with a bilinear form with signature all $1$'s except for a single $-1$ (or all $-1$'s with a single $1$) is called a Minkowski metric.