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Non-square matrix and linear independence

  1. Feb 13, 2010 #1
    Can a non square matrix have linearly independent columns? I can't take the determinant so I can't tell.
  2. jcsd
  3. Feb 13, 2010 #2
    Yes. For instance,
    [tex]\left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \\ 0 & 0 \end{array}\right][/tex]
    Of course it will have to have more rows than columns.
  4. Feb 14, 2010 #3


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    If, on the other hand, the matrix has more columns than rows, the columns cannot be independent. If there are say, m columns and n rows, with m> n, then the columns are n dimensional vectors and a set of m vectors of n dimensions, with m> n, cannot be independent.
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