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Inverse of Matrix - Product Form

  1. Apr 30, 2012 #1
    In a few books on Operations Research, I have found a reference to a method of finding the inverse of matrix using a method called as 'Product Form'. From the context, it looks like the product form method is used for finding the inverse of the basis matrix in a simplex table.
    The method may or may not work for other kind of matrices. However, I couldn't find a good description of this method. One text which mentions this is "Operations Research" by Hamdy Taha. A description of the method is supposedly given in the CD accompanying the book - but I have a hand me down book & don't have the CD. If anyone here knows more about this method or has a pointer to it, please let me know.
     
  2. jcsd
  3. May 2, 2012 #2

    Stephen Tashi

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    You can find the jargon "product form" used in articles if you search using the keywords:
    inverse matrix simplex basis product form

    As far as I can see, it simply refers to the fact that if you do elementary row operations on a matrix, the combined effect of these can be represented as a product of elementary matrices. Hence if you do Gaussian elimination on a matrix, you can keep track of the operations you do and this gives you a representation of the inverse of the matrix as a product of elementary matrices.
     
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