Invariance (Mathematics)

An property (of a mathematical object) is invariant if, after some operation(s) are applied, that property remains unchanged.

For instance, in a geometrical space where the concept of “length” is defined (by some metric); a physical object, say a pencil, will maintain its characteristics (length) despite a change of coordinates (e.g. polar to cartesian).

In short, vectors are invariant, but their components are not (under a transformation).