3
$\begingroup$

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
  • 3
    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

1 Answers 1

1

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?

  • 1
    If you are the same person as the OP, you might want to ask a moderator to merge your accounts.2010-12-31
  • 0
    @arturo how does one go about contacting a moderator on this list?2011-01-01
  • 0
    @ronaf: for a specific post or comment, With enough reputation, you can flag and call up moderator attention. Doesn't take much (15 pts). There should be an option of "needs moderator attention". Otherwise, you can try posting in meta.2011-01-01
  • 0
    @arturo the flag option i can conjure up for a comment will identify it as noise, offensive or spam. i agree that there *should* be an option "needs moderator attention". but as this doesn't seem to be a list feature at present - i suppose one needs to contact a moderator to suggest adding it. sounds like a nice catch 22 to me.2011-01-01
  • 1
    @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