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The prime examples of such four vectors are the four position and four momentum of a particle, and for fields the electromagnetic tensor and stressenergy tensor. Now, we subtract these two equations and divide by 4 to obtain that for all x,ydisplaystyle x,y of unit norm, gixyi0.displaystyle g_alpha ixalpha yi0. Finally, by successively deriv community letting xdisplaystyle x range over e1,enRndisplaystyle e_1,dots,e_nin mathbb R n and then letting ydisplaystyle y range over e1,epRpdisplaystyle e_1,dots,e_pin mathbb R p, we see that g11gnngn1,n1gnp, npdisplaystyle -g_11dots -g_nng_n1,n1dots g_np, np, or in other words, gdisplaystyle g has deriv community the matrix representation. Secure and responsible trading.
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