Similarity invariance
From Wikipedia, the free encyclopedia
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.
This article needs additional citations for verification. (November 2019) |
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
Wikiwand - on
Seamless Wikipedia browsing. On steroids.