Composing multiple Fundamental/Essential matrices

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I have computed the fundamental matrices between Frame [a,b], [b,c] and [c,d]. I have now Fab, Fbc and Fcd. Is it possible to compute Fad directly without matching? I am thinking of sth like 3D transformation composing where:

T04 = T01 * T12 * T23 * T34

I think working with fundamental matrices directly won't help. I guess the answer in Essential matrices which I can compute since I have the Camera Calibration matrix.

So, How can I combine two (or more) Fundamental or essential matrices?