What is the line $y=x$ and $y=-x$ called?

Question

I know that some non-english mathematicians use first median to mean the identity line $y=x$ (i.e. line considered in $\mathbb R^2$) and second median to mean the line $y=-x$. I don't suppose this is the same in English. Any special name for $y=-x$? Is identity line the only name for $y=x$?

Answer 1

The terms diagonal and anti-diagonal are descriptive and "culturally apt".

The first is standard in geometry and topology (the diagonal embedding of a topological space $X$ is the inclusion $X \hookrightarrow X \times X$ defined by $x \mapsto (x, x)$), and I'm almost positive I've seen the second in connection with the normal bundle of a diagonal embedding of a manifold.

In a casual web search, the primary usage of "anti-diagonal" refers to square matrices for which entries are zero unless the row and column indices are "opposites" (specifically, $a_{ij} \neq 0$ only if $j = n + 1 - i$), but even this usage suggests the line $y = -x$ by association.