Re: Solving matrix equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg53840] Re: Solving matrix equation*From*: gabyz at ee.bgu.ac.il (Gaby)*Date*: Sat, 29 Jan 2005 06:02:48 -0500 (EST)*References*: <7fh0u5$gs3@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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