The projection matrix $P = I -xx^T\in \mathbf{R}^{d \times d}$ has a zero eigenvalue and eigenvalues equal to one with multiplicity $d-1$. Is it possible to apply whitening transform on $P$ taking into consideration that the inverse of $D=diag(0,1,1,\dots, 1)$ has to be computed? Is there any way to overcome this difficulty?

Thank you in advance.


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