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The Matrix Cookbook

The Matrix Cookbook [ ]Kaare Brandt PetersenMichael Syskind PedersenVersion: November 15, 20121 IntroductionWhat is this?These pages are a collection of facts (identities, approxima-tions, inequalities, relations, ..) about matrices and matters relating to is collected in this form for the convenience of anyone who wants a quickdesktop reference .Disclaimer:The identities, approximations and relations presented here wereobviously not invented but collected, borrowed and copied from a large amountof sources. These sources include similar but shorter notes found on the internetand appendices in books - see the references for a full :Very likely there are errors, typos, and mistakes for which we apolo-gize and would be grateful to receive corrections at ongoing:The project of keeping a large repository of relations involvingmatrices is naturally ongoing and the version will be apparent from the date inthe :Your suggestion for additional content or elaboration of sometopics is most welcome algebra, Matrix relations, Matrix identities, derivative ofdeterminant, derivative of inverse Matrix , differentiate a :We would like to thank the following for contributionsand suggestions: Bill Baxter, Brian Templeton, Christian Rish j, ChristianSchr oppel, Dan Boley, Douglas L.

A B Hadamard (elementwise) product A B Kronecker product 0 The null matrix. Zero in all entries. I The identity matrix Jij The single-entry matrix, 1 at (i;j) and zero elsewhere A positive de nite matrix A diagonal matrix Petersen & Pedersen, The Matrix Cookbook, Version: November 15, 2012, Page 5

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