Matlab mldivide, minimum norm ?

Hi,

I was wondering if for an underdetermined system the Matlab mldivide 
(equivalent to \) function will retrurn the minimum norm solution, or if the 
returned solution is constrained in another way or if the solution has no 
particular properties beyond satisfying the set of equations ?

The matlab help page doesn't help me.

http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html

Thanks,

NL 

"NewLine" <umts_remove_all_this@skynet.be> wrote in message 
news:43cffb7d$0$4768$ba620e4c@news.skynet.be...
> Hi,
>
> I was wondering if for an underdetermined system the Matlab mldivide 
> (equivalent to \) function will retrurn the minimum norm solution, or if 
> the returned solution is constrained in another way or if the solution has 
> no particular properties beyond satisfying the set of equations ?
>
> The matlab help page doesn't help me.
>
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html
>
You could have a look here - http://people.csail.mit.edu/nati/mmmf/code.html

Best of luck - Mike

NewLine wrote:
> Hi,
>
> I was wondering if for an underdetermined system the Matlab mldivide
> (equivalent to \) function will retrurn the minimum norm solution, or if the
> returned solution is constrained in another way or if the solution has no
> particular properties beyond satisfying the set of equations ?
>
> The matlab help page doesn't help me.
>
> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html

>From the above link:

"If A is an m-by-n matrix with m ~= n and B is a column vector with m
components, or a matrix with several such columns, then X = A\B is the
solution in the least squares sense to the under- or overdetermined
system of equations AX = B."

>> Hi,
>>
>> I was wondering if for an underdetermined system the Matlab mldivide
>> (equivalent to \) function will retrurn the minimum norm solution, or if 
>> the
>> returned solution is constrained in another way or if the solution has no
>> particular properties beyond satisfying the set of equations ?
>>
>> The matlab help page doesn't help me.
>>
>> http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html
>
>>From the above link:
>
> "If A is an m-by-n matrix with m ~= n and B is a column vector with m
> components, or a matrix with several such columns, then X = A\B is the
> solution in the least squares sense to the under- or overdetermined
> system of equations AX = B."
>

I understand the least squares in an overdetermined system. How is a least 
squares solution defined for an underdetermined system ?
Any solution will satisfy AX-B = 0.

NewLine wrote:
...
> I understand the least squares in an overdetermined system. How is a least
> squares solution defined for an underdetermined system ?
> Any solution will satisfy AX-B = 0.

Perhaps the X with least squares norm is chosen? This is usually done
in linear least squares when the design matrix does not have full rank.