In mathematics, a trace identity is any equation involving the trace of a matrix.
Contents
Example
For example, the Cayley–Hamilton theorem says that every matrix satisfies its own characteristic polynomial.
Properties
Trace identities are invariant under simultaneous conjugation.
Uses
They are frequently used in the invariant theory of n×n matrices to find the generators and relations of the ring of invariants, and therefore are useful in answering questions similar to that posed by Hilbert's fourteenth problem.
Examples
References
Trace identity Wikipedia(Text) CC BY-SA