What does it mean for a transformation T:X→Y to be invariant?

[indigojoker]

I just wanted to know say a matrix X is invariant under some transformation T.

So:
T:X->Y is invariant...

does that mean all the elements of X are the same as the elements of Y? Or is the elements in Y a scalar multiple of the elements in X?

 

[Dick]

If a matrix (or anything else) is invariant under a transformation T, then T(X)=X. Period.