Linear Algebra and Its Applications [ペーパーバック]

The ¡°applications¡± implied by the title has a double meaning. Several simplified yet representative problems taken from engineering and economics are well presented. In addition, another major theme throughout the text is the role of linear algebra applied to other areas of mathematics; notably calculus, differential equations, and optimization. Repeatedly, the author appeals to the reader¡￣s intuition, demonstrating the boundaries between mathematical topics by comparing and contrasting the discrete and continuous case of a problem. For example, the discussion of orthogonal vectors, vector spaces, and projections quickly moves from vectors to functions once we regard functions as infinite dimensional vectors containing infinite components. The discussion eventually leads to a very intuitive take on Fourier series and Legendre polynomials in the context of orthogonal projections. Other examples abound where Strang cohesively ties together various areas of math in a perspective that isn¡￣t emphasized enough in other texts.

Hence, this is not only a book on linear algebra. To get the most out of the text requires familiarity with calculus encompassing multiple variables, vectors and some ordinary differential equations. Readers lacking this background will understand some sections only to be lost in others as coverage moves quickly from elementary concepts to topics where they have no previous exposure.

Chapters 1-5 and half of 6 comprise the core of the book. The remainder provides satisfactory coverage of numerical linear algebra, the finite element method, and linear programming. However, a more thorough treatment of these topics is deferred to Strang¡￣s companion volume, Introduction to Applied Mathematics for which the core chapters provide a good prerequisite.

One more word of caution: The author¡￣s enthusiasm of the subject is both a liability and an asset. Professor Strang sometimes has the annoying habit of summarizing the topic prior to presenting the lesson. Having to weed through his exultation to find where the lesson actually begins makes reading the book challenging at times.

While the rigor in the text may fall short of the needs of pure mathematicians, I see no reason not to recommend this book to anyone seeking a solid foundation for further study in applied mathematics. Getting through the books requires some degree of patience but it¡￣s well worth the effort.

Sure, Strang's book may not be an adequate sole text from which to learn linear algebra and matrix theory. But surely serious mathematicians (as opposed to kindergarteners) would never attempt to learn a subject from a single text.

This is where the book shines - as a supplement to a more formal text. (Here, pick your own; I have my own personal favorite, but it has been out of press for years). And then read the two side by side. One provides rigor, the other, INTUITIVE UNDERSTANDING. This, after all, is where Strang's book shines - rather than providing only a formal understanding of the mathematics in question, he manages to convey an intuitive understanding of the objects represented by linear algebra methods in many common applications.