Comments on: Woodbury Matrix Inverse Identity http://www.lindonslog.com/mathematics/woodbury-matrix-inverse-multivariate-normal/ Sun, 27 Nov 2016 15:23:00 +0000 hourly 1 https://wordpress.org/?v=4.6.1 By: michelleleighh http://www.lindonslog.com/mathematics/woodbury-matrix-inverse-multivariate-normal/#comment-310 Wed, 04 Jun 2014 10:49:55 +0000 http://www.lindonslog.com/?p=663#comment-310 Sure

]]> By: admin http://www.lindonslog.com/mathematics/woodbury-matrix-inverse-multivariate-normal/#comment-309 Tue, 03 Jun 2014 23:42:32 +0000 http://www.lindonslog.com/?p=663#comment-309 I love it, can I add it to the main post?

]]> By: michelleleighh http://www.lindonslog.com/mathematics/woodbury-matrix-inverse-multivariate-normal/#comment-306 Tue, 03 Jun 2014 21:09:48 +0000 http://www.lindonslog.com/?p=663#comment-306 Very nice series of articles about schur compliment and etc. Appreciate them very much.

Anyways here is my proof of mean1=mean2
\left[\Lambda+ X_{2}^TI_{2} X_{2}\right]^{-1} X_{2}^T\\ =\{\Lambda^{-1}-\Lambda^{-1} X_{2}^T\left[I_{2}+ X_{2}\Lambda^{-1} X_{2}^T\right]^{-1} X_{2}\Lambda^{-1}\} X_{2}^T\\ =\Lambda^{-1} X_{2}^T\left[I_{2}+ X_{2}\Lambda^{-1} X_{2}^T\right]^{-1}\left[I_{2}+ X_{2}\Lambda^{-1} X_{2}^T\right]-\Lambda^{-1} X_{2}^T\left[I_{2}+ X_{2}\Lambda^{-1} X_{2}^T\right]^{-1} X_{2}\Lambda^{-1} X_{2}^T\\ =\Lambda^{-1} X_{2}^T\left[I_{2}+ X_{2}\Lambda^{-1} X_{2}^T\right]^{-1}I_{2}

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