How to solve this matrix?

I have some variables to find like x= [1x16 (x1,x2,x3,....x16 variables)] with condition that x1+x2+x3+....x16=1. I have also 16x16 matrix Q= [16x16 (real values)]. I need to solve the equation 'x*Q=x'. How can I solve it in Matlab?

Answer 1

[James Tursa]

To get a basis for the solution space:

null(Q.' - eye(16))

Note that if Q.'-eye(16) is full rank then the only solution is a vector with all 0's.

Answer 2

[Bruno Luong]

>> P=[0.2 0.4 0.4; 1 0 0; 0.5 0.25 0.25]

P =

    0.2000    0.4000    0.4000
    1.0000         0         0
    0.5000    0.2500    0.2500

>> pi=null(P'-eye(3))';

>> pi=pi/sum(pi)

pi =

    0.4839    0.2581    0.2581

>> pi*31

ans =

   15.0000    8.0000    8.0000

>> pi*P

ans =

    0.4839    0.2581    0.2581

>>