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System of ODE's

  1. Jul 19, 2006 #1
    I am working with a system governed by the dynamics x'=Ax (prime denotes differentiation w/ respect to t) where x is a vector and A is a matrix. Given the way our data is collected we can't measure x directly but rather a scalar function D(x)=(sum of the components of the vector x). My question is: given sufficiently many data points what can we conclude about the matrix A? Can we find its entries uniquely or are we stuck with a set of infinitely many solutions? And finally how does the answer to this question depend on the structure of the matrix (distinct/repeated eigenvalues etc.)
  2. jcsd
  3. Jul 19, 2006 #2
    all you have is the D(x)=sum(x_i)? are you given x'?
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