In mathematics, a trace identity is any equation involving the trace of a matrix.

Properties

Trace identities are invariant under simultaneous conjugation.

Uses

They are frequently used in the invariant theory 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

• The Cayley–Hamilton theorem says that every square matrix satisfies its own characteristic polynomial are given by the elementary symmetric polynomials of the eigenvalues of .

• All square matrices

See also

References

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