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In mathematics, a trace identity is any equation involving the trace of a matrix.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. 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.

Examples

• By the Cayley–Hamilton theorem, all matrices satisfy

$\mathrm{t}\mathrm{r}(A^n)-\mathrm{t}\mathrm{r}(A)\mathrm{t}\mathrm{r}(A^{n-1})+\cdots +(-1{)}^n\det (A)=0.$

• All matrices satisfy

$\mathrm{t}\mathrm{r}(A)=\mathrm{t}\mathrm{r}(A^T).$

See also

• Invariant polynomial

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