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, [math]\displaystyle{ f }[/math] is invariant under similarities if [math]\displaystyle{ f(A) = f(B^{-1}AB) }[/math] where [math]\displaystyle{ 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]\displaystyle{ B^{-1}AB }[/math], where [math]\displaystyle{ B }[/math] is the transformation matrix to the new basis.
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