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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. tr(ST) = tr S.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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