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Linear Algebra: Orthogonal matrices

  1. Sep 17, 2011 #1
    1. The problem statement, all variables and given/known data

    A matrix M has an inverse iff it is of full column and row rank, and row rank = column rank. Since any orthogonal matrix has full column rank, does that imply that non-singular matrices are orthogonal as well?

  2. jcsd
  3. Sep 17, 2011 #2
    No, we have that orthogonal => full column rank. But we don't have the converse. There are non-singular matrices which are not orthogonal.
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