I totally agree for -1, this answer is not useful :)

@ Hurkyl , actually I know how to code, so I already wrote a program to do this 3D fft interms of 1D fft. But its when you start to follow those conventions and try to formulate it in math the confusion arises. For 2D its different , the way we index an array is exactly how I am writing equations. But for 3D it gets confusing, at least for me :)

Thanks Carlo. But there in lies my confusion of the answer, can I now write things more differently like this, to get $F_x$ I will sum over first argument (instead of second according to matrix indexes), $F_y$ over second and $F_z$ over third, will that be more consistent and correct ? This is confusing since I couldn't find this type of notation in any text, etc.