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
> +----------------------------------------------------------+

```

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