The determinant of a second-order tensor is also defined by the expression|S| =[(S. A) x (S B)] · (S · C)АХ В.С%3Dwhere A, B, and C are arbitrary vectors. Verify the identity in an orthonormal basis{ê;}.

We will verify the given identity in 3 dimension, and by choosing A,B,C as our orthonormal basis.

Answered: The determinant of a second-order…

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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The determinant of a second-order tensor is also defined by the expression [(S · A) × (S · B)] · (S · C) = Isl Ах В.С where A, B, and C are arbitrary vectors. Verify the identity in an orthonormal basis {êi}.