Trace identity

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In mathematics, a trace identity is any equation involving the trace of a matrix. For example, the Cayley-Hamilton theorem says that every matrix satisfies its own characteristic polynomial.

Trace identities are invariant under simultaneous conjugation. 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.

[edit] Examples

• By the Cayley-Hamilton theorem, all matrices satisfy

• Symmetric matrices satisfy

[edit] See also

• Invariant polynomial