Transcription of The Matrix Cookbook - Mathematics
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The Matrix Cookbook - Mathematics
The Matrix Cookbook [ ]. 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: 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 apolo- gize 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.
An Matrix indexed for some purpose or The n.th power of a square matrix A 1 The inverse matrix of the matrix A A+ The pseudo inverse matrix of the matrix A (see Sec. 3.6) A1=2 The square root of a matrix (if unique), not elementwise (A) ij The (i;j).th entry of the matrix A A ij The (i;j).th entry of the matrix A [A] ij The ij-submatrix, i.e. A ...
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