Linear Algebra with Applications: .

by Gareth Williams

Linear Algebra with Applications, Ninth Edition is designed for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics. Updated to increase clarity and improve student learning, the author provides a flexible blend of theory and engaging applications. The material in Linear Algebra with Applications, Ninth Edition is arranged into three parts that contain core and optional sections: Part 1 introduces the basics, discussing systems of linear equations, vectors in Rn matrices, linear transformations, determinants, eigenvalues, and eigenspaces. Part 2 builds on this material to discuss general vector spaces, and includes such topics as the Rank/Nullity Theorem, inner products and coordinate representation. Part 3 completes the course with important ideas and methods in Numerical Linear Algebra including ill-conditioning, pivoting, LU decomposition and Singular Value Decomposition. Throughout the text the author provides interesting applications, ranging from theoretical applications such as the use of linear algebra in differential equations, to many practical applications in the fields of electrical engineering, traffic analysis, relativity, history, and more.

Genres: Mathematics, Textbooks

594 pages, Hardcover

First published January 1, 1984

Reviews

[Barrett Barry · Rating 5 out of 5]

This is great as an introduction to linear algebra or for someone who wants to know how to use linear algebra to solve practical problems. Every chapter ends with applications such as using markov chains to quantify population movements and genetics, google, weather prediction, cryptography (hamming codes), Quadratic forms (relativity) , difference equations, normal modes, economics, fractals, traffic flow, electrical networks. This is an essential book in my opinion.

[Teddy · Rating 3 out of 5]

An interestingly formatted book- touches briefly on topics like linear independence, and determinants in the first couple of chapters, then re-covers them a few chapters later. Not as useful as just covering any given topic all at once, I think.

The problems were also not quite ideal- either too easy (trivial computations) or too difficult (abstract proofs). This book definitely works best if you've already had a proofs class.

That said, explanations of concepts were pretty clear, examples were useful, and the text was very readable. There were also optional sections on practical applications of linear algebra, which were neat to read

Overall, a good reference book and source for problems, but not what I'd choose for a primary text.