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Question on decomposition of a matrix

  1. Apr 8, 2014 #1

    I have a [itex]2\times 2[/itex] real matrix [itex]M[/itex] such that: [tex]M=A^T \Sigma A[/tex], where the matrix [itex]\Sigma[/itex] is symmetric positive definite, and [itex]A[/itex] is an arbitrary 2x2 nonsingular matrix. Both A and ∑ are unknown, and I only know the entries of the matrix M itself. Note that M is symmetric positive definite too.

    I was wondering if it is possible to apply some decomposition of the matrix [itex]M[/itex] in order to find another matrix [itex]P_M[/itex] such that: [tex]P_M = AQ[/tex]
    where the matrix Q must not depend on A (e.g. it cannot be a product of matrices where A appears). I basically want to find a matrix PM where the multiplication with A appears only at the left side, and not at both sides like in M.
    Last edited: Apr 8, 2014
  2. jcsd
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