Re: Solving matrix equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg29986] Re: Solving matrix equations*From*: axc at poincare.EECS.cwru.edu*Date*: Fri, 20 Jul 2001 03:28:49 -0400 (EDT)*Organization*: Case Western Reserve University*References*: <9j0h2b$fij$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

this equation is consistent if A has a unit eigenvalue and the eigenspace corresponding to this eigenvalue intersects the affine space defined by One.x=1 (i.e x1+...+xn=1, One is the all-ones vector). if this is true, the solution is unique when the dimension of the eigenspace is 1. however if it's greater than one (implying the unit eigenvalue has alg. multiplicity >1) then the solution is not a point but the entire intersection of this eigenspace with the affine space One.x=1. alan calvitti axc at eecs.cwru.edu "Christopher Deacon" <cdeacon at nospam.physics.mun.ca> writes: > How can I solve the matrix equation x = A.x, where x is a vector (x1, x2, x3 > ,...) and > x1+x2+x3 ... = 1? > > Chris > > -- > +-----------------------------+----------------------------+ > | Christopher Deacon | (709) 737-7631 > | Dept of Physics and Physical| cdeacon at physics.mun.ca > | Oceanography > | Memorial University of Nfld > +----------------------------+-----------------------------+ > | http://www.physics.mun.ca/~cdeacon > +----------------------------------------------------------+