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Explicit expression for inverse of I-A

  1. Nov 19, 2012 #1
    Hello,
    This is not a homework exercise, so I decided to post it here. Hopefully one of you could help.
    I would like to find an explicit expression for (I-A)^(-1), provided that A is a squared matrix (nxn) and A^k = 0. It is also given that I-A^k = (I-A)(I+A+A^2+...+A^(k-1)).
    I understand that by definition the inverse matrix of I-A will be (I+A+A^2+...+A^(k-1)), but is there a way to arrive at a more simplified, explicit expression (yet without knowing what A is)?
     
  2. jcsd
  3. Nov 19, 2012 #2

    micromass

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    I don't understand why

    [tex]I+A+A^2+...+A^{k-1}[/tex]

    isn't good enough for you. It's an explicit expression.

    To my knowledge, there is no other expression.
     
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