# Projection matrix

#### squenshl

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.

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#### Peeter

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.

#### squenshl

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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