The Matrix Cookbook [ http://matrixcookbook.com ] Kaare Brandt Petersen Michael Syskind Pedersen Version: November 15, 2012 1 Introduction What is this? These pages are a collection of facts (identities, approxima- tions, inequalities, relations, ...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference . Disclaimer: Theidentities, approximations and relations presented here were obviously not invented but collected, borrowed and copied from a large amount of ...
The Matrix Cookbook Kaare Brandt Petersen Michael Syskind Pedersen Version: February 16, 2006 What is this? These pages are a collection of facts (identities, approxima- tions, inequalities, relations, ...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference . Disclaimer: Theidentities, approximations and relations presented here were obviously not invented but collected, borrowed and copied from a large amount of sources. These sources include similar but ...
Pacic Graphics 2016 Volume 35 (2016), Number 7 E. Grinspun, B. Bickel, and Y. Dobashi (Guest Editors) SupplementaryMaterial 1041 In this supplementary material, we provide a proof for Eq. 7 in equal to U (C) up to scale, where µ guarantees the unity determinant c our manuscript. Note this proof is the discrete analogy of Sec. 3 constraint. Thus: in [RA15]. −1 1 −1 ( ) =|Uc(C)|d Uc (C). Lemma:ForaxedclusterC,the minimization of our dened color homogeneity, which ...
1 The Matrix Cookbook a 1 a Notation : A vector a = 2 always denotes a row-vector. With aT = [a ,a ,...,a ] we will . 1 2 d . . a d denote a column vector. Transpose : T T T T T T −1 T T −1 −T (A+B) =A +B , (AB) =B A , (A ) =(A ) =A (1) Product : (AB) =XA B (2) ij ik ki k (AB)C=A(BC), AB6=BA (3) Inner product of ...
Natural Gradients Made Quick and Dirty: Companion Cookbook Jascha Sohl-Dickstein January 23, 2010 1 Recipes and tricks 1.1 Natural gradient The natural gradient is ˜ −1 ∇ J(θ)=G (θ)∇ J(θ) (1) θ θ where J (θ) is an objective function to be minimized with parameters θ, and G(θ) is a metric on the parameter space. Learning should be performed with an update rule ˜ θ =θ +θ (2) t+1 t t ˜ &tilde ...
The Matrix Cookbook Kaare Brandt Petersen Michael Syskind Pedersen Version: January 5, 2005 What is this? These pages are a collection of facts (identities, approxima- tions, inequalities, relations, ...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference . Disclaimer: Theidentities, approximations and relations presented here were obviously not invented but collected, borrowed and copied from a large amount of sources. These sources include similar but ...
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