Publisher:

Chapman & Hall/CRC

Number of Pages:

725

Price:

99.95

ISBN:

9781584887829

How many books on introductory linear algebra exceed the 725 pages of this one? At a guess, none. Of such books, how many exclude coverage of standard topics such as the Gram-Schmidt process, quadratic forms, hermitian and unitary matrices and Jordan forms etc? In my estimation, only a strict minority. Is there any other book that concentrates so heavily on establishing the concepts the basic concepts of linear algebra? I very much doubt it.

By way of illustration, the first four hundred pages of Larry Knop’s book are devoted to eliciting the concept of vector space. The treatment begins with revision of elementary vector algebra in **R**^{2} and generalises such properties to **R**^{n}. In fact, up to page 146, everything is kept at an intuitively practical level prior to the emergence of vector space axioms. Subsequently, the notions of subspace, spanning sets, linear independence, and bases are carefully elicited and not until page 391 is it felt safe to introduce the ideas and methodology of linear transformations.

So, after 520 pages of lively narrative, and hundreds of exercises and examples, one encounters the two remaining chapters on Determinants and Eigenspaces respectively. The remaining sixty pages are allocated to the solutions of selected exercises.

I have to say that I’m very much in favour of this approach to the teaching of linear algebra because, recalling my own introduction to the subject (about 200 years ago, it seems), and recalling courses that I have designed and taught to undergraduates, the mistake was to proceed too rapidly through the early stages, and move on to more advanced techniques too quickly.

Consequently, the thickness of this book is partly due to the nature of its expositional narrative, which is almost conversational, and it aims to get students to read more independently and of their own volition (this always begins with an element of directed reading of course).

Another appealing feature of Larry Knop’s book is the range and quality of the illustrations and the myriad of applications that appear from the earliest chapters onwards.

To summarize, by limiting the mathematical scope of this book, and by carefully smoothing the path from the particular to the general, the author has provided an alternative approach to linear algebra that will be of interest to many of those who currently teach it.

The very first lecture on linear algebra that **Peter Ruane** received as a student began with a delineation of the axioms and a range of theorems with no motivational material whatever (and certainly no applications).

Date Received:

Monday, September 8, 2008

Reviewable:

Yes

Series:

Textbooks in Mathematics 2

Publication Date:

2009

Format:

Hardcover

Audience:

P. N. Ruane

01/19/2009

Logical Foundations

Logical Equivalences

Sets and Set Notation

Quantification

The Vector Space R

The Vector Space R

The Vector Spaces R

The Vector Spaces R

The Vector Spaces R

Vector Spaces: Setting the Rules

Vector Spaces: On the Wild Side

Subspaces

Subspaces and Linear Equations

Subspaces from Subsets

Solving Linear Systems

Systematic Solutions of Systems

Technology and Linear Algebra

Spanning Sets

Linear Independence

More on Linear Independence

Linear Independence and Span

Vector Space Bases

The Dimension of a Vector Space

Transformation Fundamentals

Vector Space Isomorphisms

Matrix Representations of Transformations

Matrices and Associated Vector Spaces

Inverses in Matrix Multiplication

Elementary Matrices

An Introduction to Determinants

Properties of Determinants

Eigenvalues, Eigenvectors, and Eigenspaces

More on Eigenvalues, Eigenvectors, and Eigenspaces

Forests, Digraphs, and PageRank

Diagonalization

Publish Book:

Modify Date:

Monday, January 19, 2009

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