Unformatted text preview: epqj = 2oij. 4. Show that .
c . CT = CT,.; C = 8,
ecker delta.
where C is the direction cosine matrx and 8 is the matrx of the Kron use it
Any matrx obeying spch a relationship is called an orthogonal matri beca
represents transformation of one set of ortogonal axes into another.
5. Show that for a secondorder tensor A, the following thee quantities are Multiplication and Contraction of Tensors invarant under the rotation of axes: II = AÂ¡Â¡ I A.2 A33 A31 Al3
/z = I Aii A12 I + A32 A23/ + I AiiA33 1
A21 A22
13 = det(AÂ¡j). 4 3. Prove the following relationships: Ch 2: Problem 4
OijOij = 3 epqrepqr = 6
epqÂ¡epqj = 2oij. 4. Show that .
c . CT = CT,.; C = 8,
ecker delta.
where C is the direction cosine matrx and 8 is the matrx of the Kron use it
Any matrx obeying spch a relationship is called an orthogonal matri beca
represents transformation of one set of ortogonal axes into another.
5. Show that for a secondorder tensor A, the following thee quantities are
invarant under the rotation of axes: II = AÂ¡Â...
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This document was uploaded on 02/28/2014 for the course PHYS 4200 at Columbia.
 Spring '14
 MichaelMauel
 Physics

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