profile-img
Tanishka yadav Asked a Question
July 22, 2021 9:58 pmpts 30 pts
Diagonal and Trace Let A = [a,] be an n-square matrix. The diagonal or main diagonal of A Consists of the eleme- with the same subscripts, that is, a22 ag3 a The trace of A, written tr(A), is the sum of the diagonal elements. Namely, +nn tr(A) = a, t az2 +ags t+ an Theorem: Suppose A = [a] and B = [b,] are n-square matrices and k is a scalar. Then () The following theorem applies. tr(AT) = tr(A), tr(AB) = tr(BA). (ii) tr(A + B) = tr(A) + tr(B), tr(kA) = k tr(A), (iv) (i) A 2 3 2. Then and B =0 Example: Let A =| 6 2 1 5 and tr(A) = 1 - 4+7 = 4 tr(B) = 2 +3 - 4 = 1 diagonal of A = {1, 4, 7} and diagonal of B = {2, 3,-4) tr(A + B) = 3- 1 +3 5. tr(2A) = = 2 - 8+ 14 8. tr(AT) = 1 - 4+7 = tr(AB) = 5+ 0 - 35 =-30, tr(BA) = 27 24-33 =-30 Moreover, As expected from Theorem, tr(A +B) = tr(A) + tr(B), tr(AT) = tr(A), tr(2A) = 2 tr(A) Furthermore, although AB # BA, the traces are equal.
  • 1 Answer(s)
  • 0 Likes
  • 1 Comments
  • Shares
  • Alka gupta thankyou
    yes, given theorem is absolutely correct and examples are also correct no single mistake in solution...
    Likes(0) Reply(1)
    Tanishka yadav
    plss aap mujhe ye theorem or examples smjha do mujhe smjh nhi aya
Head Office :
MPA 44, 2nd floor, Rangbari Main Road,
Mahaveer Nagar II, Kota (Raj.) – 324005

Corporate Office:
212, F-1, 2nd Floor, Evershine Tower,
Amrapali Marg,
Vaishali Nagar, Jaipur (Raj.) – 302021

Mail: info@eduncle.com
All Rights Reserved © Eduncle.com