Translation invariant function

1. What is invariant in a translation?
2. What is invariant in translation maths?
3. Which properties are invariant under a translation?
4. What is time translation invariance?

What is invariant in a translation?

Translation invariance means that the system produces exactly the same response, regardless of how its input is shifted.

What is invariant in translation maths?

In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations of a certain type are applied to the objects.

Which properties are invariant under a translation?

Under translation lengths, areas, angles and orientation do not change.

What is time translation invariance?

Time translation symmetry is the law that the laws of physics are unchanged (i.e. invariant) under such a transformation. Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history.