How do I solve QA = R with unknown Q.

R and A are matrices with dimension 27x6, while Q is a squared matrice with dimension 27x27. Q is the only matrice which is unknown.

We know that Q*A = R.

Its simple math to solve those equations by hand, but it would take me days because of the 27 dimension.

Is there a matlab function for that?

[David K.]

I am not entirely certain so you will have to check it with smaller matrices you know the answer to, but I believe this will work:

Q = R\A;

-Note this is in fact \ and not /.

[David Goodmanson]

It's the right idea, but to get the dimensions to come out right it is going to be Q = R/A (right division of both Q*A and R by A).

The resulting Q is far from unique, though. And I believe that process only works anyway if A has at least as many linearly independent columns as R does. In other words rank(A) >= rank(B).

[Elias Ghalib]

Hey David,

you are right. R/A and not R\A gives me a solution for QA = R.

But the problem is, as you mentioned, that Q is faaaaar from unique and also from being orthogonal. I need Q to be so. Do you have any idea how to do this?

By the way, all colums of A are linearly independent, so this is no problem

[David Goodmanson]

It's not true that Q is orthogonal in general. A necessary condition is A'A = R'R, so is that the case?