- #1
ThirdEyeBlind
- 12
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Homework Statement
I'm supposed to prove [itex]det A = \frac{1}{6} \epsilon_{ijk} \epsilon_{pqr} A_{ip} A_{jq} A_{kr} [/itex] using the triple scalar product.
Homework Equations
[itex] \frac{1}{6} \epsilon_{ijk} \epsilon_{pqr} A_{ip} A_{jq} A_{ kr} [/itex]
[itex] (\vec u \times \vec v) \cdot \vec w = u_i v_j w_k \epsilon_{ijk} [/itex]
The Attempt at a Solution
I have written out and understand that [itex]det A = \epsilon_{ijk} A_{1i} A_{2j} A_{3k} [/itex] but I don't understand where the triple scalar product comes into play.
I see the similarity between the shorthand notations of the triple scalar product and the determinant but don't see how I can relate the two. I figure I must be missing some geometric/mathematical interpretation that can help me.
I've used Einstein summation notation in a couple previous problems but this is really the first involved problem I have to do and am a bit lost as to what to do.