similarity invariance

{{sources|date=November 2019}}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.