Introduction to Linear Algebra is a comprehensive text that covers the core material for linear algebra. Its author has gone to great lengths to ensure that the contents of this book are broken up into concise sections, yet the book itself retains four overall themes - linear systems, least squares, eigenvalues and singular values - and develops them with a natural progression.
Linear algebra is a subject that is compulsory in most mathematical degree programmes. Gilbert Strang's book contains enough material to be of use to anyone during his or her first two courses in the subject and, as such, it is aimed at first-year mathematicians, in the main. However, the final chapters do diversify a little via sections on computer graphics and Fourier transforms, and an exploration of how linear algebra can be applied to numerical problems. This gives the book a little more longevity.
Each chapter has a preface that serves as a synopsis of the mathematics to come. Rather than concerning itself with technical details, we are led, hand-in-hand, through a moral overview of what is trying to be achieved, rather than simply how. I found this to be a good way of introducing new mathematics - one gets a feeling for what's going on, even if the mathematical details may be initially complicated to the reader.
The mathematics itself is explained slowly and carefully. The reader is presented with little questions to encourage thinking about the ideas that are being developed, and the book has plenty of diagrams in order to help the reader visualise the problems. The content generally goes beyond the scope of what a first year would need to know in order to pass the relevant courses. Each section concludes with a bullet-point review of the key ideas, and then presents worked examples as well as "challenge problems" that the reader can work on.
Overall, Introduction to Linear Algebra covers this key branch of mathematics well. It is delivered at a good pace for its target audience and covers enough material to make the book worth purchasing. I see it being useful to those who feel they need extra help learning first-year courses.
Who is it for? First-year mathematics undergraduates.
Presentation: Clear and concise with plenty of diagrams.
Would you recommend it? To first-year undergraduates only. Not worth the money for second year and above.
Introduction to Linear Algebra
Author: Gilbert Strang
Publisher: Wellesley Cambridge Press