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Matrix multiplication preserve order Block matrix

  1. Aug 1, 2011 #1
    Hello,

    If I have block matrices A,B,C and D all of which are non singular would this relationship hold; my main concern is preserving order of matrix multiplication:

    if ADB=C

    then AD=B^-1C
    D=B^-1CA^-1
    D^-1 = (BC^-1A)


    Also is it okay to assume the inverse of a block matrix is equal to a matrix that contains as its elements the inverse of each individual block?

    Thanks for any help

    Emma
     
  2. jcsd
  3. Aug 1, 2011 #2

    I like Serena

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    Homework Helper

    Hi EmmaSaunders1! :smile:

    Your multiplications are a little off.
    They should be:

    ADB=C
    ADBB-1=CB-1
    AD=CB-1
    D=A-1CB-1
    D-1 = (BC-1A)

    You can check the last step by calculating DD-1.

    (Btw, you can use the x2 just above the reply box to get nice superscripts. :wink:)


    And yes, it is okay to assume the inverse of a block matrix is equal to a matrix that contains as its elements the inverse of each individual block.
    You can check this by creating an example, and see how the matrices multiply.
     
  4. Aug 1, 2011 #3
    Thats great thanks for that
     
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