most recent 30 from http://mathoverflow.net 2013-05-22T19:14:55Z http://mathoverflow.net/feeds/question/99135 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99135/reference-for-this-qr-perturbation-result Alex Gittens 2012-06-08T17:04:03Z 2012-06-08T17:04:03Z

<p>I believe this result is due to Stewart, but I haven't been able to track it down: let $A$ have full column rank and let $B = A + E$ where $P_{A} E = 0$. Then $$ \|(I - P_B)P_A\|^2_2 = 1 - \lambda_{\text{min}}(A(B^TB)^{-1} A^T) $$</p> <p>Any idea where it's stated? And any extensions?</p>