# 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, is invariant under similarities if where 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 , where is the transformation matrix to the new base.