# 4 dimensional curl as antisymmetric matrix

by purplegreen
Tags: antisymmetric, curl, dimensional, matrix
 P: 4 I'm a bit confused. I'm trying to calculate the curl of a 4 dimensional matrix. It's an attempt to use stokes theorem for 4 dimensions. The curl can be written as a antisymmetric matrix from what I understand with entries, Mi,j = d Ai/d j - dAj/di where i and j would be the different coordinates like x, y, z etc... However, from what I understood if you looked the integral about an infinitesimal square in the x-y plane you could work out the integral as: (dAy/d x - dAx/dy)ΔxΔy I was informed that this would gives M1,2 ΔxΔy which would be wrong, you would get -M12 surely? So how does the curl look in matrix/ tensor form for 4 dimensions? Hopefully this makes some sense, sorry if it's a slightly confused question.

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