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 A B ) where B − 1 A B is a matrix similar to A. Examples of such functions include the trace, determinant, 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 base is related to one in the old base by the conjugation B − 1 A B , where B is the transformation matrix to the new base.