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Matrix Algebra

  1. Sep 30, 2005 #1
    I have to calculate the trace of the following matrix: [tex](A+I)^{-1}[/tex]
    where [tex]A[/tex] is:
    [tex]1 0 0 1[/tex]
    [tex]0 2 2 0[/tex]
    [tex]0 2 2 0[/tex]
    [tex]1 0 0 1[/tex]
    and [tex]I[/tex] is the unit matrix 4x4.
    The calculations are extremely excruciating and the result is [tex]38/15[/tex] [checked]. I'm afraid I miss the whole point of this. Can the fact the matrix is diagonalizable help me reach the answer faster?
    I mean not going through the process of adding 1 to the diagonal elements and do the inverse.

    Thank you.
  2. jcsd
  3. Sep 30, 2005 #2


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    Staff Emeritus
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    Gold Member

    It would if you could get the trace of A from its diagonalization!
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