Similarity invariance

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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, 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}AB , where  B is the transformation matrix to the new base.

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