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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

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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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Yes, Z has full rank, and A is positive definite, but using the formula I do not get how i can compute $(A Z^T Z A)^+ $ as a function of $(Z^T Z)^+ $ and $A$... or am I doing something wrong?

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    @ronaf: that's for comments. If you flag a post, there is "needs moderator attention". And there's always meta: there should be a link at the very top that says "meta", just left of "faq". You can post a question there.2011-01-01