Moore-Penrose pseudo inverse - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-18T16:57:49Z http://mathoverflow.net/feeds/question/50743 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/50743/moore-penrose-pseudo-inverse Moore-Penrose pseudo inverse Liliana 2010-12-30T17:39:04Z 2011-01-27T23:22:14Z <p>I have a matrix Z n times p with p>n</p> <p>I have A a diagonal matrix with positive entries</p> <p>I would like to know if there is a knwon relation (as a function of A) between</p> <p>the MP inverse of Z^T Z</p> <p>and the MP inverse of A Z^T Z A</p> <p>what i am looking for is the follwing: suppose I knwo the MP of $Z^T Z$ and I know $A$, can I get as a function of those two things the MP inverse of $A Z^T Z A$?</p> http://mathoverflow.net/questions/50743/moore-penrose-pseudo-inverse/50745#50745 Answer by optima for Moore-Penrose pseudo inverse optima 2010-12-30T17:58:33Z 2010-12-30T17:58:33Z <p>If by 'knwon relation' you mean whether you can convert between these matrices unambiguously then the answer is yes. The Moore-Penrose pseudoinverse always exists and is unique, and A is nonsingular. That is all you need.</p> http://mathoverflow.net/questions/50743/moore-penrose-pseudo-inverse/50771#50771 Answer by maxdev for Moore-Penrose pseudo inverse maxdev 2010-12-30T22:54:31Z 2010-12-30T22:54:31Z <p>"what i am looking for is what is suppose I know the MP of Z^T Z, how can i get the MP of A Z^T Z A using A and the MP of Z^T Z? thanks"</p> <p>$(A Z^T Z A)^\dagger = (A ((Z^TZ)^\dagger)^\dagger A)^\dagger$</p>