Similarity invariance
Encyclopedia
In mathematics
, 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 similarity of 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."
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, 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 similarity of A. Examples of such functions include the trace, determinantDeterminant
In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...
, and the minimal polynomial
Minimal polynomial (linear algebra)
In linear algebra, the minimal polynomial of an n-by-n matrix A over a field F is the monic polynomial P over F of least degree such that P=0...
. A more colloquial phrase that means the same thing as similarity invariance is "basis independence."