need perfect work ....

Physics
Tutor: None Selected Time limit: 1 Day

Show that if A is similar to B, then Tr(A) = Tr(B).

Show that if A is Diagonalizable, then Tr(A) is the sum of the eigenvalues.

Jul 24th, 2015

Thank you for the opportunity to help you with your question!

if A is diagonalizable then let the diagonal entries be a(ii) for i=1, ..., n. then Tr(A) = Σa(ii) ie sum over i.

and the eigen values are roots of equation

(a(11)-λ) (a(22)-λ) ... (a(nn)-λ) = 0

which will give n roots same as a(11) , ... , a(nn)

so Tr(A) is sum of eigenvalues.

View comments (1)


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 24th, 2015

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Jul 24th, 2015
...
Jul 24th, 2015
Dec 5th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer