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Linear Algebra and Linear Models (Universitext), by Ravindra B. Bapat
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Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included.
For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include:
coverage of topics such as rank additivity, inequalities for eigenvalues and singular values;
a new chapter on linear mixed models;
over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices.
This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.
- Sales Rank: #3524989 in Books
- Published on: 2012-02-12
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .40" w x 6.10" l, .56 pounds
- Binding: Paperback
- 167 pages
Review
From the book reviews:
“The author presents basic ideas and concepts of linear algebra and linear models equally from both theoretical and applications perspectives. … This book is well presented and structured for an upper level undergraduate course for students of statistics. Further, it can serve as a textbook for an entry-level graduate course. Not only that, it can act as a reference book for practitioners and research statisticians.” (Technometrics, Vol. 55 (1), August, 2012)
From the Back Cover
Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included.
For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include:
• coverage of topics such as rank additivity, inequalities for eigenvalues and singular values;
• a new chapter on linear mixed models;
• over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices.
This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.
Most helpful customer reviews
0 of 0 people found the following review helpful.
A good review book
By Pavel Nadin
The good thing about this book is it's short and affordable. The bad is everything else. If you're new to the advanced concepts, and you're not a braniac, like most of us, this book is not for you. It's better suited as a review book, not a study book. When a concept is introduced, there's no "story" with it. No motivation for the concept is given, the idea is presented on its own, often out of context, and you sit wondering "why do I need to know this??" Furthermore, if you like studying by examples, forget it. All you get is a short dry definition (or a theorem with a proof), and off you go. To be fair, there are very few examples, but nearly not as much as needed to illustrate the concept for somebody who is learning the idea for the first time. So I ended up using the book as a reference of what I have to know for my class, and learning the material from other sources.
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