to find eigen value crieteria for parron frobinious theory

[ayina]

hi what is significance of eigen value criteria af some arbitrary matrix. i m using this in expession P=inv(I-A)*B. where A is 4x4 matrix and B is vector of 4x1. i wanna satisfy eigen value vriteria using parron frobinius theory . could some help ? i m waiting for reply

 

[weetabixharry]

i m using this in expession P=inv(I-A)*B

You need to describe exactly what you're trying to do in more detail, then I might be able to help.

Eigenvalues go together with eigenvectors. For a given square matrix, M, the non-zero vector v is an eigenvector of M if it has the special property that:

Mv = λv​

where λ is a scalar, called the eigenvalue (corresponding to v).

Eigenvalues and eigenvectors have extremely wide-ranging and profound uses. Please describe the problem you are trying to solve and we'll see if they can help.

 

[ayina]

i m solving resource allocation problem for d2d communication (wireless problem) in which after solving the whole framework i got matrix A and B . where for matlab simulation purpose P is initialized basically it is power optimization problem. here is paper i m tring to reproduce its results. P=int*P+N finding parron frobenious criteria to find probability of local communicicaion.
int_ul =

[ 0 0 0 1.0185
0 0 0 0
0.8478 0.8407 0 1.0123
0.9818 0 0 0]

N_ul =

1.0e-08 *

[ 0.0414
0
0.1736
0.0422]
P=[15 15 15 15]';initialized problem

 

[weetabixharry]

In the paper, they define "eigenvalue criteria" as being satisfied if r < 1. This just ensures there is a positive solution to Equation 11. Then, you need to solve the minimisation problem in Equation 12.

I only had a couple of minutes to look at the paper, so I'm not sure if they say what method they use for the minimisation. There may be an analytical solution, or they may have resorted to solving numerically.

 

[ayina]

thanks bur what is r here. i thought its dominant eigen value of matrix (i mentioned as 'int') . but if that is rue then there is no solution for which this (r<1) is satisfied. that is basic problem. if i dont found that then proceeding that paper wouldn't an easy task. while thanks\


this matrix has e =

0 0 0 0
0 1.0 0 0
0 0 -1.00 0
0 0 0 0 and r=1; means criteria is not satisfied