Doing some last minute homework, and stuck on this one. Although its due in 4 hours thought its worth a shot.
Our assignment is to "Use a property of determinants to show that A and A^T have the same characteristic polynomial."
I know that (A - LI)x = 0, where L = lambda.
Not sure how to prove that with something like
det(A-LI) = 0? No idea.
Also, one other: Show that if A and B are similar, then det A = det B
Put B=A-LI, now det(B)=det(B'), so:
Originally Posted by Ideasman
So the charateristic polynomial of A' (which is det(A'+LI)) is equal to
det(B'), which is equal to det(B) which is the charateristic polynomial of A
(that is: det(A-LI)).