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I have an $n\times p$ matrix $Z$ with $p\gt n$.

I have a diagonal matrix $A$ with positive entries.

Is there is a known way to determine the MP inverse of $A Z^T Z A$, if I know $A$ and the MP inverse of $Z^T Z$.

Thanks

  • 0
    Does $\mathbf Z^T$ have full rank?2010-12-31
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    This [article](http://dx.doi.org/10.1137/1006007) by R.E. Cline gives an expression for the pseudoinverse of the product of two matrices: $$(\mathbf A\mathbf B)^+=(\mathbf A^+\mathbf A\mathbf B)^+(\mathbf A\mathbf B(\mathbf A^+\mathbf A\mathbf B)^+)^+$$2010-12-31

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