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Rank of skew symmetric matrix

  1. Dec 14, 2013 #1
    What is minimum possible rank of skew symmetric matrix ?
     
  2. jcsd
  3. Dec 14, 2013 #2

    jgens

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    Look at the zero matrix.
     
  4. Dec 14, 2013 #3
    But how can we say that zero matrix is skew symmetric matrix
     
  5. Dec 14, 2013 #4

    jgens

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    If 0 denotes the zero matrix, then 0T + 0 = 0. So this matrix is skew-symmetric.
     
  6. Dec 14, 2013 #5

    mathwonk

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    a little more surprising question might be what is the maximum rank, say of a 3by3 skew symmetric matrix?
     
  7. Dec 14, 2013 #6
    Determinant of skew symmetric matrix of odd order is always zero. So for skew symmetric matrix its rank will be always even in number. ..
     
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