Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Science Advisor

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook