Similarity invariance

In linear algebra, similarity invariance is a property exhibited by a function whose value is unchanged under similarities of its domain. That is, $$f$$ is invariant under similarities if $$f(A) = f(B^{-1}AB)$$ where $$B^{-1}AB$$ is a matrix similar to A. Examples of such functions include the trace, determinant, characteristic polynomial, and the minimal polynomial.

A more colloquial phrase that means the same thing as similarity invariance is "basis independence", since a matrix can be regarded as a linear operator, written in a certain basis, and the same operator in a new basis is related to one in the old basis by the conjugation $$B^{-1}AB$$, where $$B$$ is the transformation matrix to the new basis.