solve quadratic set of equations

I have a system of equation which i would like to solven this systme can be expressed as :

w=(w1,...,wn)' and let consider a symmetric matrix n*n Σ(s), i would like to solve a system as :

ω(s) ω(s)’= inverse (Σ(s)).

can someone give a program/command to solve this kind of systems

[Torsten]

In my opinion, left and right hand side can never be equal since the matrix on the left has rank 1 whereas the matrix on the right has rank n.

[Walter Roberson]

Since w is defined as the transpose of a row vector, it follows that w is n x 1. w * w' would then be (n x 1) * (1 * n) which would be n x n.

However, the amount of information in w * w' would be n, where-as the amount of information in the inverse of a symmetric matrix is the same as the amount of information in the symmetric matrix, which is potentially n * (n-1) / 2. It therefore seems likely that there will not usually be a solution.

[tilfani oussama]

The amount of information would in both sides woul be n*(n-1)/2 as inverse Σ(s) and w * w' are both symmetric

[Torsten]

Using w*w' for a vector w, you can only generate symmetric matrices of rank 1.

Your right-hand side is a matrix of rank n.

Believe us: Your system can't be solved for s unless n=1.

Best wishes

Torsten.

Answer 1

[tilfani oussama]

Let me expose the problem from the beginning. My aim is to solve for w=(w1,...,wn)' an optimization problem, the probelm can be expressed as :

Max E(Rp(s))

subject to

 k(s)=(ω(s)'Σ(s)ω(s))^(1/2)
 e’ω(s) + υ(s) = 1

Let fix parameter s, and solve for one s value

 Σ(s) = Ω(s) + σm2(s) β(s)*β(s)’  
 β(s)=(β1(s),....,βn(s))'

and Ω(s) = diag(a1,...,an) with all elements are positives.

and

   E(Rp(s)) = ω(s)’c + ω(s)’β(s)Rm + υ(s)Rf

with Rm and Rf are knowns.

[Torsten]

Try "fmincon".

[tilfani oussama]

thank you for your reply, can you tell me more. Bests

[Torsten]

Just make an attempt to set up the problem for "fmincon" and come back if you encounter specific problems.

Best wishes

Torsten.