The Matrix Cookbook is a reference book containing identities, approximations, inequalities, and relations about matrices and related topics. It is intended as a quick desktop reference for anyone needing matrix-related information. The content is collected from various sources, including internet notes and book appendices. The authors apologize for any errors and welcome corrections. The book is continuously updated and includes sections on basics, derivatives, inverses, complex matrices, solutions and decompositions, statistics and probability, multivariate distributions, Gaussians, special matrices, functions and operators, and more. It covers topics such as trace, determinant, eigenvalues, derivatives of determinants and inverses, matrix norms, and various matrix decompositions like LU, LDM, and singular value decomposition. The book also includes properties of special matrices, such as orthogonal, symmetric, and idempotent matrices. It provides formulas for derivatives of matrix expressions, including those involving traces, norms, and eigenvalues. The authors acknowledge contributions from many individuals and thank The Oticon Foundation for funding their PhD studies. The book is written for researchers and practitioners in fields requiring matrix algebra, including statistics, machine learning, and signal processing.The Matrix Cookbook is a reference book containing identities, approximations, inequalities, and relations about matrices and related topics. It is intended as a quick desktop reference for anyone needing matrix-related information. The content is collected from various sources, including internet notes and book appendices. The authors apologize for any errors and welcome corrections. The book is continuously updated and includes sections on basics, derivatives, inverses, complex matrices, solutions and decompositions, statistics and probability, multivariate distributions, Gaussians, special matrices, functions and operators, and more. It covers topics such as trace, determinant, eigenvalues, derivatives of determinants and inverses, matrix norms, and various matrix decompositions like LU, LDM, and singular value decomposition. The book also includes properties of special matrices, such as orthogonal, symmetric, and idempotent matrices. It provides formulas for derivatives of matrix expressions, including those involving traces, norms, and eigenvalues. The authors acknowledge contributions from many individuals and thank The Oticon Foundation for funding their PhD studies. The book is written for researchers and practitioners in fields requiring matrix algebra, including statistics, machine learning, and signal processing.