Matrix Equation Help?

Dear R-listers

Now I have a Matrix Equation to solve,
A -- m by n matrix, where n>>m, known matrix;
X -- n by m unknown matrix;
B -- m by m known matrix.

So given the equation A*X=B, how to solve X?

I first tried to take X = inv((A'*A))*A'. But since
A'*A is singular, this is no way to go.

Please give me some point on this.
Thanks

Fred

Feng Zhang wrote:

Dear R-listers

Now I have a Matrix Equation to solve,
A -- m by n matrix, where n>>m, known matrix;
X -- n by m unknown matrix;
B -- m by m known matrix.

So given the equation A*X=B, how to solve X?

You already mentioned it:
?solve

Uwe Ligges

I first tried to take X = inv((A'*A))*A'. But since
A'*A is singular, this is no way to go.

Please give me some point on this.
Thanks

Fred

If n>>m, then solve does not work.  Consider:

 > A <- array(1:6, dim=c(2,3))
 > B <- array(1:4, dim=c(2,2))
 > solve(A, B)

Error in solve.default(A, B) : singular matrix `a' in solve

In this case, we have 6 = 3 x 2 unknowns but only 4 equations.

It raises questions about what you mean by solve.  S-Plus 2000 and 6 
have "ginverse" that will produce an answer.  You can construct such 
using "qr" or "svd".

However, before coding that, I will ask, what do you mean by "solve"?

hth.  spencer graves

Uwe Ligges wrote:

Feng Zhang wrote:

Dear R-listers

Now I have a Matrix Equation to solve,
A -- m by n matrix, where n>>m, known matrix;
X -- n by m unknown matrix;
B -- m by m known matrix.

So given the equation A*X=B, how to solve X?

You already mentioned it:
?solve

Uwe Ligges

I first tried to take X = inv((A'*A))*A'. But since
A'*A is singular, this is no way to go.

Please give me some point on this.
Thanks

Fred

If n>>m, then solve does not work.  Consider:

 > A <- array(1:6, dim=c(2,3))
 > B <- array(1:4, dim=c(2,2))
 > solve(A, B)

Error in solve.default(A, B) : singular matrix `a' in solve

In this case, we have 6 = 3 x 2 unknowns but only 4 equations.

It raises questions about what you mean by solve.  S-Plus 2000 and 6
have "ginverse" that will produce an answer.  You can construct such
using "qr" or "svd".

However, before coding that, I will ask, what do you mean by "solve"?

hth.  spencer graves

Uwe Ligges wrote:

Feng Zhang wrote:

Dear R-listers

Now I have a Matrix Equation to solve,
A -- m by n matrix, where n>>m, known matrix;
X -- n by m unknown matrix;
B -- m by m known matrix.

So given the equation A*X=B, how to solve X?

You already mentioned it:
?solve

Uwe Ligges

I first tried to take X = inv((A'*A))*A'. But since
A'*A is singular, this is no way to go.

Please give me some point on this.
Thanks

Fred