Similarity invariance

In mathematics, 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 similarity of 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."

See also

• Invariant (mathematics)
• Gauge invariance
• Trace diagram