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Determinant identity

  1. Aug 17, 2011 #1

    quasar987

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    Hello matrices masters,

    If A and B are nxn square matrices, is there an identity for the determinant of the block matrix

    A -B
    B A

    ?

    Lots of thanks and praises.
     
  2. jcsd
  3. Aug 17, 2011 #2

    CompuChip

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    Would http://www.mth.kcl.ac.uk/~jrs/gazette/blocks.pdf [Broken] be able to help you out?
     
    Last edited by a moderator: May 5, 2017
  4. Aug 17, 2011 #3

    Ben Niehoff

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  5. Aug 18, 2011 #4

    quasar987

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    Unfortunately, in the particular case I'm interested in, I don't see a reason to believe that A and B commute, nor that A or B is invertible. So none of the formulae on wiki are applicable.

    I know for a fact that the determinant of that matrix is nonzero, and it is probably positive, which I am trying to show.
     
  6. Aug 19, 2011 #5
    Did you try finding a pattern between the 2x2, 4x4, 9x9?
     
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