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The Matrix Cookbook

[ ]
Kaare Brandt Petersen
Michael Syskind Pedersen
Version: November 14, 2008
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

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
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: Bill Baxter, Brian Templeton, Christian Rishøj, Christian
Schr¨oppel Douglas L. Theobald, Esben Hoegh-Rasmussen, Glynne Casteel, Jan
Larsen, Jun Bin Gao, J¨urgen Struckmeier, Kamil Dedecius, Korbinian Strimmer,
Lars Christiansen, Lars Kai Hansen, Leland Wilkinson, Liguo He, Loic
Thibaut, Miguel Bar˜ao, Ole Winther, Pavel Sakov, Stephan Hattinger, Vasile
Sima, Vincent Rabaud, Zhaoshui He. We would also like thank The Oticon
Foundation for funding our PhD studies.   Tell A Friend