Matrix Algebra: Exercises and Solutions

ISBN-13: 9780387953182 / Angielski / Miękka / 2001 / 271 str.

David A. Harville; D. a. Harville

Opis

This book comprises well over three-hundred exercises in matrix algebra and their solutions. The exercises are taken from my earlier book Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to make them comprehensible independently of their source. To further insure that the restated exercises have this stand-alone property, I have included in the front matter a section on terminology and another on notation. These sections provide definitions, descriptions, comments, or explanatory material pertaining to certain terms and notational symbols and conventions from Matrix Algebra From a Statistician's Perspective that may be unfamiliar to a nonreader of that book or that may differ in generality or other respects from those to which he/she is accustomed. For example, the section on terminology includes an entry for scalar and one for matrix. These are standard terms, but their use herein (and in Matrix Algebra From a Statistician's Perspective) is restricted to real numbers and to rectangular arrays of real numbers, whereas in various other presentations, a scalar may be a complex number or more generally a member of a field, and a matrix may be a rectangular array of such entities.

Recenzje

From the reviews of the first edition:

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"...written as a companion to his earlier book titled MATRIX ALGEBRA FROM A STATISTICIAN'S PERSPECTIVE...this is not just a solutions manual. With 15 pages of definitions and terminology and another 5 pages of notations, the book can be used as an independent reader on advanced topics in linear algebra...when used in conjunction with his earlier book, provides a more in-depth second course on this topic."

"This book collects the exercises from the author's Matrix algebra from a statistician's perspective, (Springer 1997) and includes their solutions. ... It can be used as a stand-alone book with an inspiring collection of exercises ... ." (Adhemar Bultheel, Simon Stevin Bulletin, Vol. 10 (2), 2003)

"The author has collected well over 300 exercises from his earlier book Matrix Algebra From a Statistician's Perspective into a separate volume and he added solutions. The book also contains extensive and detailed summaries of the relevant terminology and notation. ... It will be very useful for any teacher of a linear algebra course as a source of exercises of various levels of difficulty." (European Mathematical Society Newsletter, December, 2003)

"This book comprises well over 300 exercises in (real) matrix algebra and their solutions. ... it represents a valuable resource for any reader trying to gain some practice in the concepts of matrix algebra and looking for suitable exercises accompanied by solutions." (A. Kräuter, Internationale Mathematische Nachrichten, Vol. 57 (193), 2003)

"This book is a supplement to the author's previous book (Harville 1997) and contains the solutions to more than three-hundred exercises taken from it. ... This book is especially useful for anyone interested in dealing with proof techniques and tricks concerning matrix algebra. ... For everybody who finds pleasure in reading and learning from Harville's text, this book will have a similar effect and should be viewed as a very useful supplement." (Jürgen Groß, Statistical Papers, Vol. 43 (4), 2002)

Spis treści

1 Matrices.- 2 Submatrices and Partitioned Matrices.- 3 Linear Dependence and Independence.- 4 Linear Spaces: Rowand Column Spaces.- 5 Trace of a (Square) Matrix.- 6 Geometrical Considerations.- 7 Linear Systems : Consistency and Compatibility.- 8 Inverse Matrices.- 9 Generalized Inverses.- 10 Idempotent Matrices.- 11 Linear Systems: Solutions.- 12 Projections and Projection Matrices.- 13 Determinants.- 14 Linear, Bilinear, and Quadratic Forms.- 15 Matrix Differentiation.- 16 Kronecker Products and the Vec and Vech Operators.- 17 Intersections and Sums of Subspaces.- 18 Sums (and Differences) of Matrices.- 19 Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints.- 20 The Moore-Penrose Inverse.- 21 Eigenvalues and Eigenvectors.- 22 Linear Transformations.- References.