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Re: Solving matrix equation


On 20 Apr 1999 00:48:05 -0400, Oldfield So wrote:
>Dear all,
>
>I need to solve a equation in the following format:
>
>	 M A = A
>
>where M is a rectangular matrix, A is a column vector.  By using
Solve[], 
>the following "error" is obtained:
>
>RowReduce::luc: 
>   Result for RowReduce of badly conditioned matrix {<<12>>}
>     may contain significant numerical errors.
>
>I would like to know is there any standard way to solve it?  Thanks a
lot.
>
>Best Regards,
>Oldfield So
>-- 
>Oldfield K.Y. SO | kysoNOspam at cse.cuhk.eduDOThk | <a
href="http://www.cse.cuhk.edu.hk/~kyso";>http://www.cse.cuhk.edu.hk/~kyso</a>

Yes\
There is a usual way to solve it:
I suggest you first reaquinte yourself with eigenvalues and eigen
vectors theory.

M*x=s*x
where "s" is an eigenvalue, and "x" is an eigenvector (if A is
rectangular then your eigne values are the values in the main
diagonal)
since M is invertable you have N (the dimension of M) solutions of
that are:

M*(sqrt(s)*x) = (sqrt(s)*x)

Gaby


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