Problem #1: A rank two tensor L is given as: 7 10 3 L = L = 4 -1 -2 9 4 5 (a) Calculate the symmetric (S) and skew-symmetric or antisymmetric

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 6AEXP
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Problem #1: A rank two tensor L is given as:
[7 10 3
L = L =|4
-1 -2
9 4
5
(a) Calculate the symmetric (S) and skew-symmetric or antisymmetric (
(b) Calculate the three invariants of S and W tensors.
(c) Show the following:
(i) tr(SW) = 0
(ii) det(S') det(S)
(iii) det(S') = (detS)'
Transcribed Image Text:Problem #1: A rank two tensor L is given as: [7 10 3 L = L =|4 -1 -2 9 4 5 (a) Calculate the symmetric (S) and skew-symmetric or antisymmetric ( (b) Calculate the three invariants of S and W tensors. (c) Show the following: (i) tr(SW) = 0 (ii) det(S') det(S) (iii) det(S') = (detS)'
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