Thread Subject: Solving equation

equation : A=x*B

where A=3x8 ; B=3x8 and variable x= 3x3 matrix

How can i solve this equation to find x when A and B are known?

since i can't find inverse of B as its not a square matrix.

"Maruti " <marutiagarwal@mathworks.com> wrote in message
<fkrdub$62d$1@fred.mathworks.com>...
> equation : A=x*B
>
> where A=3x8 ; B=3x8 and variable x= 3x3 matrix
>
> How can i solve this equation to find x when A and B are
known?
>
> since i can't find inverse of B as its not a square matrix.
>

x = A*B'*pinv(B*B');

Anh Huy Phan
RIKEN - BSI

x=A/B %%% <- (B'\A')'

This gives solution in the leastsquare sense, i.e., each row
of A will be approximate by each-row of x*B in the
leastsquare sense. In other word each element R reaches the
minimum (for all possible 3x3 x)

R=sum((A-x*B).^2,2)

Bruno

"Huy " <phananhhuy@mathworks.com> wrote in message
<fkrf5j$34f$1@fred.mathworks.com>...
> "Maruti " <marutiagarwal@mathworks.com> wrote in message
> <fkrdub$62d$1@fred.mathworks.com>...
> > equation : A=x*B
> >
> > where A=3x8 ; B=3x8 and variable x= 3x3 matrix
> >
> > How can i solve this equation to find x when A and B are
> known?
> >
> > since i can't find inverse of B as its not a square matrix.
> >
>
> x = A*B'*pinv(B*B');

Actually, this is not a good way to solve the problem.
This squares the condition number, leaving you
with a potentially inaccurate solution.

If you will use pinv in the first place, why not use
its full capability?

x = A*pinv(B);

HTH,
John