let A be an nxn matric and the trace of A is defined by tr(A)= a_11+a_22...+a_nn . Prove that the coeff of x^(n-1) in the characteristic polynomial is -tr(A)
We have
and the terms we haven't written have degree .
Regards.
Fernando Revilla
Another method (the first is similar to that of Dr. Revilla's) is that you can first recall that is monic and it's roots are precisely the mulitiset spectrum of . and so
We can then recall Vieta's formula so that (remembering that is monic) that where is the first symmetric polynomial. Thus,