In mathematics, a trace identity is any equation involving the trace of a matrix.
Properties edit
Trace identities are invariant under simultaneous conjugation.
Uses edit
They are frequently used in the invariant theory of 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 edit
- The Cayley–Hamilton theorem says that every square matrix satisfies its own characteristic polynomial. This also implies that all square matrices satisfy
- All square matrices satisfy
See also edit
- Trace inequality – inequalities involving linear operators on Hilbert spaces
References edit
Rowen, Louis Halle (2008), Graduate Algebra: Noncommutative View, Graduate Studies in Mathematics, vol. 2, American Mathematical Society, p. 412, ISBN 9780821841532.