2.53 Prove the following identities when A and B are vectors and S, R, and T are second- order tensors: (a) tr(AB) = A.B. tr(ST) = tr S.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 34E
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2.53 Prove the following identities when A and B are vectors and S, R, and T are second-
order tensors:
(a) tr(AB) = A.B.
(c) tr(RS) = R.S.
(e) tr(R.S) = tr(S. R).
(b)
tr(ST) = = tr S.
(d)
tr(RT.S) = R: S.
(f) tr(R.S.T) = tr(T.R.S) = tr(S. T-R).
Transcribed Image Text:2.53 Prove the following identities when A and B are vectors and S, R, and T are second- order tensors: (a) tr(AB) = A.B. (c) tr(RS) = R.S. (e) tr(R.S) = tr(S. R). (b) tr(ST) = = tr S. (d) tr(RT.S) = R: S. (f) tr(R.S.T) = tr(T.R.S) = tr(S. T-R).
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