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Linear Algebra Question

  1. Feb 16, 2012 #1
    Let’s say that we have a constant matrix A which is the coefficients matrix and column vector U of control variable as well as column vector X of state variables:
    The question is: What is the proper technique in Linear Algebra that I should do to know which element in U has the most impact on the corresponding perturbed element in X.
    On other words, there is an element in X has been perturbed and I would like to correct it by adjusting a few (as less as I can) elements in U.
    I know the maximum element in the corresponding row of A which is multiplied by U column vector would have the most effect and by that I will know the corresponding element in U, but I am searching about a formal linear algebra technique to deal with this not algorithmic or programming procedure
  2. jcsd
  3. Feb 17, 2012 #2


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    Science Advisor

    Just an idea:

    Is the matrix A diagonalizable? If so, maybe the diagonal form would make it
    clearer .
  4. Feb 17, 2012 #3
    If A is invertible, then the adjustment is unique, if A is rank deficient, the adjustment can be made minimal in L2 norm if you use pseudoinverse, if you want minimal L1 norm adjustment, you go with nonlinear optimization.
  5. Feb 19, 2012 #4
    i appreciate it. Thanx
  6. Feb 19, 2012 #5
    How can I do that by using singular value decomposition?
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