I'm curious as to how the following proof is verified. I have toiled over this thing for quite a while, but haven't made any progress. I don't need a step-by-step solution, but I would appreciate any help getting it started:(adsbygoogle = window.adsbygoogle || []).push({});

Given the following:

Qis an orthogonal tensor

eis a unit vector such that_{1}Qe=_{1}e_{1}

nis of unit length and orthogonal toe_{1}

mis such thatm[tex]\bullet[/tex]e= 0,_{1}m = Qnandm[tex]\bullet[/tex]n= cos[tex]\theta[/tex]

1is the identity matrix

Prove that:

Q=1cos[tex]\theta[/tex] + (1-cos[tex]\theta[/tex])e- (_{1}[tex]\otimes[/tex]e_{1}e-_{2}[tex]\otimes[/tex]e_{3}e_{3}[tex]\otimes[/tex]e_{2})sin[tex]\theta[/tex]

Whereeform an orthonormal triad and_{1}, e_{2}, and e_{3}

[tex]\otimes[/tex] represents the dyadic product

My apologies if this is the wrong thread to post this at, but I looked around and couldn't find any threads on this topic.

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# Homework Help: Orthogonal Tensor Proof

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