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The axes Ox′1x′2x′3are obtained from Ox1x2x3 by a rotation through an angle αabout Ox3. If σ′ij...

The axes Ox′1x′2x′3are obtained from Ox1x2x3 by a rotation through an angle αabout Ox3. If σ′ij and σij are the components of the stress tensor with respect to these axes,show that

σ′11+σ′22 = σ11 + σ22,

σ′13 + iσ′23 = e−iα13+iσ23)

σ′11−σ′22+ 2iσ′12=e−2iα11−σ22+ 2iσ12).

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