Help with analyzing the transpose of an adjoint

Question

anonymous · Answer

When taking the transverse, is it done after the adjoint of gBC and Fc?
$$F ^{B} = Ad _{g ^{B}_{C}}^{T} * F ^{C}$$

anonymous · Answer

It's actually transpose. You transpose the adjoint matrix in this formula (before multiplying by F^X). If you didn't do that, you would end up with a 1x3 vector, which is not what you want.

anonymous · Answer

I meant transpose, sorry. But how would that work? I thought adjoining $$g ^{B}_{C}$$ with $$F ^{C}$$ would look like this $$g ^{B}_{C} * F ^{C} * g ^{C}_{B}$$ so wouldn't it only be possible to transpose after doing that multiplication?

anonymous · Answer

In last week's homework, there was a formula for the SE2 adjoint matrix. It's just a matrix multiplication. You can transpose the adjoint matrix first.

jaynator495 · Answer

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