The Matrix Cookbook

Abstract

What is this? These pages are a collection of facts (identities, approximations , 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: The identities, 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 shorter notes found on the internet and appendices in books-see the references for a full list. Errors: Very likely there are errors, typos, and mistakes for which we apologize and would be grateful to receive corrections at cookbook@2302.dk. Its ongoing: The project of keeping a large repository of relations involving matrices is naturally ongoing and the version will be apparent from the date in the header. Suggestions: Your suggestion for additional content or elaboration of some topics is most welcome at cookbook@2302.dk. Keywords: Matrix algebra, matrix relations, matrix identities, derivative of determinant, derivative of inverse matrix, differentiate a matrix. Acknowledgements: We would like to thank the following for contributions and suggestions: Christian Rishøj, Douglas L. Theobald, Esben Hoegh-Rasmussen, Lars Christiansen, and Vasile Sima. We would also like thank The Oticon Foundation for funding our PhD studies.