Handbook of Matrices

Matrices are used in many fields such as statistics, econometrics, mathematics, natural sciences and engineering. They provide a concise, simple method for describing long and complicated computations. This is a comprehensive handbook and dictionary of terms for matrix theory. Definitions, Notations, Terminology.

Rules for Matrix Operations.

Matrix Valued Functions of a Matrix.

Trace, Determinant and Rank of a Matrix.

Eigenvalues and Singular Values.

Matrix Decompositions and Canonical Forms.

Vectorization Operators.

Vector and Matrix Norms.

Properties of Special Matrices.

Vector and Matrix Derivatives.

Polynomials, Power Series and Matrices.

Appendix.

References.

Index.

Helmut Lütkepohl is a German econometrician specializing in time series analysis. Since January 2012, he has been Bundesbank Professor in the field of "Methods of Empirical Economics" at the Free University of Berlin and Dean of the Graduate Center at the German Institute for Economic Research.

Matrices are used in many areas such as staustics, econometrics, mathematics, natural sciences and engineering. This handbook provides a collection of numerous results for easy reference in one source, together with a comprehensive dictionary of matrices and related terms. The book is structured and cross-referenced so that specific results and information are easy to locate References for proofs and computational algorithms are provided. Researchers, professionals and students using matrix techniques will find this book to be an invaluable resource for their work. Contents

• Definitions, Notation, Terminology
• Rules for Matrix Operations
• Matrix Valued Functions of a Matrix
• Trace, Determinant and Rank of a Matrix
• Eigenvalues and Singular Values
• Matrix Decompositions and Canonical Forms
• Vectorization Operators
• Vector and Matrix Norms
• Properties of Special Matrices
• Vector and Matrix Derivatives
• Polynomials, Power Series and Matrices

Appendix References Index A Dictionary of Matrices and Related Terms