A principal aim of the author of this book is to make the material accessible to the reader who is not a mathematician, without loss of mathematical rigor. The work succeeds in this ambition; in particular, no prior understanding of matrix theory at any level is required for entry into Robinson’s linear algebra overview.
The book is an introductory linear algebra text well-balanced with expository applications at each step. Applications used run the gamut of widget production, population change over time, battlefield scenarios, and more. While such applications are illustrative of the relevant method or theorem, they are the minority of the examples given in the book. The majority of examples and exercises are mechanical implementation of topics specific to the section.
I am reviewing the hardcover edition of the book, which I find very easy to read. I mean this physically, with the eyes. Whereas most textbooks I find tend toward stark white paper, thin fonts and thinner paper, this book has a physical makeup like what might be used for a novel. The lightly cream-colored thick pages along with the choice of font make the book easier to read.
The book starts from the basic definition of a matrix and of matrix operations. These preliminaries even introduce matrices over rings and fields, although this group theory direction is not picked up in any significant way later in the book, except for a section in the chapter on linear transformations.
After covering systems of linear equations through Gaussian elimination and elementary row operations, the text devotes an entire chapter of about thirty pages to determinants. Robinson carefully brings in the relevant permutation theory, etc., and as a result ideas such as Cramer’s Rule can become intuitive to the diligent reader. Similar care is taken over two chapters introducing vector spaces, subspaces, etc. Orthogonality in vector spaces is also given a thorough introduction and thus well justifies introducing the least squares method in a complete fashion.
A chapter on eigenvalues and eigenvectors also introduces Markov processes and prepares the reader for two closing chapters touching on symmetric and Hermitian matrices, quadratic forms, bilinear forms, Jordan normal form, and linear programming through to the Simplex Algorithm. (The linear programming material forms the core of the additions to this edition from the first edition.)
Overall, this book can serve well as a one semester introductory course in linear algebra, or a complete package for self-study for even the uninitiated.
Tom Schulte lives and diagonalizes in Michigan, where he is a graduate mathematics student at Oakland University.