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## Main Question or Discussion Point

I have PTV=R where P and T are square matrices (4x4) and V and R are non-square (4x3).

P and V are known, T is unknown, and R is partially known (3 unknown elements).

Seems impossible, but T is a transformation matrix (ie upperleft 3x3 is a rotation matrix) which gives me additional clues.

I'm trying to find T, but I can't figure out how to approach this problem. It's been almost 10 years since I took linear algebra course and I feel very lost.

Seems like I can just rearrange it like so:

T = P'RV' where P' and V' are inverses of P and V respectively but V is non-square so I can only get left-inverse. I don't think pseudoinverse of V is the answer because I'm afraid I'll end up with overdetermined system and the whole thing becomes unsolvable.

Can anyone nudge me in the right direction? Thanks.

P and V are known, T is unknown, and R is partially known (3 unknown elements).

Seems impossible, but T is a transformation matrix (ie upperleft 3x3 is a rotation matrix) which gives me additional clues.

I'm trying to find T, but I can't figure out how to approach this problem. It's been almost 10 years since I took linear algebra course and I feel very lost.

Seems like I can just rearrange it like so:

T = P'RV' where P' and V' are inverses of P and V respectively but V is non-square so I can only get left-inverse. I don't think pseudoinverse of V is the answer because I'm afraid I'll end up with overdetermined system and the whole thing becomes unsolvable.

Can anyone nudge me in the right direction? Thanks.