The Matrix Cookbook has been updated with correction of typos and some minor additions on
We sincerely hope you will benefit from the cookbook and join the community effort by reporting typos and submit suggestions.
Thanks to Professor Ralf Östermark, Åbo Akademi University, we have become aware of an error in the derivative of Mixtures of Gaussian in section 8.4.2 (version sep 2007). The derivative of the density with respect to the mean vector, should not have a minus sign, and the correct formula are:
It is equation (315) in the image above which have been corrected (above formula is correct).
We apologize for the inconvenience and will of course make sure the error will be corrected in the next updated version of “The Matrix Cookbook”.
As we were gearing up to celebration of download number 100.000, things suddenly changed fast: In one hectic week several hundred thousands downloads erupted out of nowhere, boosting the total far beyond 400.000. Looking errornous or at least unregular in some way, we are looking into what happened, but have not yet finished that part.
We are happy to announce that The Matrix Cookbook has been updated for a September 2007 version. This version includes new material on topics like the Schur complement, Cramers rule, othorgonal matrices, matrix- and vector norms, etc. Also a few errors has been corrected.
The Matrix Cookbook has now passed to 70K mark. That is, since the announcement of the first version in 2004, The Matrix Cookbook has been downloaded by users all over the world more than 70,000 times. That makes the document the most downloaded document in history, at the institute “Informatics and Mathematical Modelling”, Technical University of Denmark.
Al though, in all fairness, it should be said that some of these hits are the same people downloading it more than once, it is true that The Matrix Cookbook has become a success in many branches of science from quantum mechanics, to econometrics and neurocomputations. We, the proud authors, are wishing all users the best of luck with the matrix computations around the world.
We have received a question from Nathan Litke, which you all are most welcome to help out on. It is regarding so-called adjugate matrices:
“I need the derivative of the adjugate matrix, e.g. Adj([a b; c d]) = [d -b; -c a]. Are you aware of a formula for this derivative, which is valid for non-singular and singular matrices?”
The Matrix Cookbook has received a question on an issue on which we would appreciate your help: the derivatives of eigenvalues.
Has anyone worked with differentiation of eigenvalues and eigenvectors with respect to the matrix elements? Note, that one may assume the matrix to be symmetric or hermitian if needed or easier. Comments are most welcome.
We have decided to spice up The Matrix Cookbook website in order to involve the cookbook users more actively in the development. We are still working on layout and functionalities of the website, so please send us your ideas …
