Solution of a matrix equation
 

Hi Guys,
I am currently doing some analysis that requires me to solve the following matrix equation:

ri = v * Ai * v'

where ri is a scalar, there are many of these (>n) and they are all known.
v is a row vector [v1 v2 ... vn], v' is it's transpose.
Ai is an n*n matrix corresponding to the ri values, these are all known.

The matrices Ai are symmetrical, real and all elements are positive.

I am trying to solve this equation for the vector v. Does anyone know of a simple method to solve this, or is anyone aware of online notes that may be able to help?

Many thanks,
B

You have a number of equations of quatratic forms. You can use Newton Approch:

f_i(v)=ri - v.Ai.v'

F = [ f_1 , ... , f_n ]

N(v)=v-(DF^(-1)(v))*F(v)

where DF^(-1)(v) is the inverse of DF (gradient of F).
Start with some v*