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Projection matrix

  1. Aug 11, 2009 #1
    I know that P = A(ATA)-1AT for a projection matrix.
    I was just wanting to know how to describe the matrix A as general as possible. For example do the columns and rows of A have to be linearly independant?
    Also I know that P = BBT is the projection matrix but how could I describe B as well.
     
  2. jcsd
  3. Aug 12, 2009 #2
    The columns of A have to be linearly independent (so that A^T A is invertable). There's an alternate projection operator for linearly dependent rows. Sounds like B B^T is only a projector if A^{-1} = A^T.
     
  4. Aug 13, 2009 #3
    Does anyone think the dimension of the column space & the dimension of the rowspace or rank or anything like that has any validation.
     
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