Elementary Matrix Theory (Dover Books on Mathematics) by Howard Eves (PDF)

Description

The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum.This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves’ book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineering, business and the social sciences, as well as math majors. Although the treatment is fundamental — no previous courses in abstract algebra are required — it is also flexible: each chapter includes special material for advanced students interested in deeper study or application of the theory.The book begins with preliminary remarks that set the stage for the author’s concrete approach to matrix theory and the consideration of matrices as hypercomplex numbers. Dr. Eves then goes on to cover fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, similarity and congruence. A final optional chapter considers matrix theory from a generalized or abstract viewpoint, extending it to arbitrary number rings and fields, vector spaces and linear transformations of vector spaces. The author’s concluding remarks direct the interested student to possible avenues of further study in matrix theory, while an extensive bibliography rounds out the book.Students of matrix theory will especially appreciate the many excellent problems (solutions not provided) included in each chapter, which are not just routine calculation exercises, but involve proof and extension of the concepts and material of the text. Scientists, engineers, economists and others whose work involves this important area of mathematics, will welcome the variety of special types of matrices and determinants discussed, which make the book not only a comprehensive introduction to the field, but a valuable resource and reference work.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is not really a beginner’s book. But it is certainly not an advanced book. It has more numerous practical hands-on exercises than an abstract algebra book would have. But it has some abstract algebra which beginner’s books would not have. It also presents complex matrices side by side with real matrices throughout. And there are numerous “Addenda”, which are more advanced extensions at the end of each chapter.This 1966 textbook by Eves shows how to perform various practical matrix procedures by hand, which nowadays would be done on computers. However, doing matrix operations by hand is a good way to understand the concepts better.The table of contents of this book gives a very good idea of its contents. So no summary is required here. The historical notes in Chapter 0 contain various details which I have not seen in other matrix algebra books. The author refers to a wide range of applications for matrices, many of which I’ve not seen mentioned elsewhere.Chapter 1 presents matrix multiplication, which is closely linked to linear transformations, as pointed out on pages 43-44. But then on pages 44-46, the use of matrices for bilinear forms is presented. This shows the real danger of trying to present matrix algebra in the absence of the underlying linear algebra abstraction. For example, matrix multiplication is not of great relevance to the matrices of bilinear forms. Many of the common matrix operations are relevant to only one of these two contexts. For example, Chapter 2 presents row operations, which are important for the solutions of systems of linear equations y=Ax, but these operations do not have the same sort of significance for bilinear forms f(x,y)=x^TAy.This book is apparently intended primarily as a kind of “service course” textbook. In other words, it is intended for students in other subjects who do not intend to become mathematicians. Perhaps nowadays with computers, this fairly practical book is less relevant. However, I think that in conjunction with other books, it’s a great way to get some background, particularly hands-on computation to make abstract concepts more concrete.

⭐This was a purchase for my children as I like them to keep reading and learning to further their education. They enjoyed it.

⭐This book was a waste of money. The author does not know how to communicate with an average reader. So much for calling itself “Elementary” …

⭐I love this book. It contains a wealth of information on basic matrix theory that one almost never gets in the classroom or typical undergraduate texts. I never realised how rich the theory of matrix theory was until I read this book. Bare in mind, however, that this is not a text on linear algebra . . . the author does touch upon the subject, but even then it is linear algebra in the context of matrix theory and not matrices in the context of linear algebra. This is rather an old approach, but one I think that is very enlightening. The author touches on advanced topics such as Lie products, Hamilton products, tensor products and so on. I this way, the student learns that the traditional way of multiplying matrices is not the only way, but simply the way that linear algebra chooses to make use of the matrices. The level of the book is undegraduate, so that any intelligent high school student should be able to get much out of the book. No real math background is required, although it would be helpful. Theory is paid attention to, but a great deal of detail is also given worked out problems, making it ideal for math students who don’t yet feel comfortable with advanced theoretical math.

⭐This is best mathematics book I’ve ever read. Eves presents his thoughts clearly and natural way, making it a comfortable reading experience.The book has widened my understanding about matrixes.

⭐First class.Very well elucidated.

Keywords

Free Download Elementary Matrix Theory (Dover Books on Mathematics) in PDF format
Elementary Matrix Theory (Dover Books on Mathematics) PDF Free Download
Download Elementary Matrix Theory (Dover Books on Mathematics) 2012 PDF Free
Elementary Matrix Theory (Dover Books on Mathematics) 2012 PDF Free Download
Download Elementary Matrix Theory (Dover Books on Mathematics) PDF
Free Download Ebook Elementary Matrix Theory (Dover Books on Mathematics)