Similarity invariance
Template:SourcesIn linear algebra, similarity invariance is a property exhibited by a function whose value is unchanged under similarities of its domain. That is, <math>f</math> is invariant under similarities if <math>f(A) = f(B^{-1}AB)</math> where <math>B^{-1}AB</math> 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 <math>B^{-1}AB</math>, where <math>B</math> is the transformation matrix to the new basis.