Question

A matrix operator when operates on a function it does not change its length, but it changes its orientation(Direction), what kind of matrix is it?

Answer 1

it's a rotation

Answer 2

@James : Yea obviously rotation, but does it have any special name in physics?

Answer 3

Actually, there's two concepts going on here. If we're talking about vectors in R^2, R^3, R^n, C^n; then changing its direction has a geometric meaning.

But when you say changing (or not) the direction of a function, what do you mean by that? I take it then that the function is a vector in some vector space of functions, in which we do not typically ascribe direction.

In other words, your question doesn't quite make sense.