rank of a matrix

Discussion in 'Math' started by sadaf, Aug 9, 2010.

  1. sadaf

    Thread Starter New Member

    Aug 4, 2010
    25
    0
    How can we find out the rank of a rectangular matrix?
    Please explain with example...?
     
  2. mik3

    Senior Member

    Feb 4, 2008
    4,846
    63
    Use Matlab!
     
  3. Papabravo

    Expert

    Feb 24, 2006
    10,138
    1,789
    The rank of a matrix is the maximum number of independent rows.

    For a square matrix you can compute the determinant to see if all the rows are independent. If the determinant is non-zero then the matrix is non-singular and the rank n is equal to the number of rows.
     
  4. sadaf

    Thread Starter New Member

    Aug 4, 2010
    25
    0
    Ok you mean to say that we can't find the rank of a rectangular matrix or a rectangular matrix doesn't have rank.
    please clear my this point because i have asked about the rectangular matrix, not about the square matrix.........?
    THANX
     
  5. Papabravo

    Expert

    Feb 24, 2006
    10,138
    1,789
    Reread my previous answer please. The answer I gave had two parts:

    The square matrix is a special case of the rectangular matrix where the determinant can be used to determine if the rows of that square matrix are independent. Determinants don't work for rectangular matrices. So you have to use other methods to determine the maximum number of independent rows. If you reduce the rectangular matrix to row echelon form you will have your answer by inspection: counting the non-zero rows.

    I trust you know what row echelon form is.
     
    Last edited: Aug 12, 2010
Loading...