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Fastest way to find inverse of 4x4 matrix?

  1. Sep 18, 2012 #1
    What is the fastest way to find the inverse of a 4x4 matrix?

    The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.
  2. jcsd
  3. Sep 18, 2012 #2


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    It is often (but not always) faster to use the determinant and the adjugate matrix.
  4. Sep 19, 2012 #3

    Ray Vickson

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    It is hardly ever faster to use determinants. You would need to calculate 16 determinants, each of which is 3x3, so each involves 9 three-factor multiplications, plus keeping track of signs and worrying about roundoff error effects. Direct row-reduction is likely much faster in the vast majority of cases. And, yes, it can involve a lot of work, but that's life!

  5. Sep 19, 2012 #4


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    Personally, I've always felt that row-reducing was faster than finding the determinant.
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