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, 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 , where is the transformation matrix to the new basis.
See also[]
- Invariant (mathematics)
- Gauge invariance
- Trace diagram
Categories:
- Functions and mappings
- Mathematical analysis stubs