Matrix Algebra
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"Gentle has put in a lot of time and effort to writing this book with careful attention to details. . it is all needed to make sure the student has a firm and solid understanding of matrix algebra on the graduate level. I would recommend this book for all those who teach graduate level matrix algebra or . to those undergraduate students who wish to have an independent study." (Peter Olszewski, MAA Reviews, January, 2018)"Beautifully written, easy to read, with a well subindexed index of 16 pages and a bibliography of 13 that includes most modern and relevant textbooks and articles in the area of matrix theory and computations, as well as for statistics and big data computations." (Frank Uhlig, zbMATH 1386.15002, 2018)
"This very reader-friendly written volume presents an opportunity to graduate students and researchers to enjoy reading on the classical matrix analysis in its modern applications to statistics and to implement thesemethods in practical problem solving." (Stan Lipovetsky, Technometrics, Vol. 60 (2), 2018)
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Content
Part I Linear Algebra.- 1 Basic Vector/Matrix Structure and Notation.- 2 Vectors and Vector Spaces.- 3 Basic Properties of Matrices.- 4 Vector/Matrix Derivatives and Integrals.- 5 Matrix Transformations and Factorizations.- 6 Solution of Linear Systems.- 7 Evaluation of Eigenvalues and Eigenvectors.- Part II Applications in Data Analysis.- 8 Special Matrices and Operations Useful in Modeling andData Analysis.- 9 Selected Applications in Statistics.- Part III Numerical Methods and Software.- 10 Numerical Methods.- 11 Numerical Linear Algebra.- 12 Software for Numerical Linear Algebra.- Appendices and Back Matter.- Bibliography.- Index.
