Applied Linear Algebra [Olver]

[mklabgr]

Applied Linear Algebra
Authors: Peter J. Olver, Chehrzad Shakiban
Publication date: 30 May 2018 (eBook)
Publisher: Springer Cham
Edition: 2nd edition
Series:Undergraduate Texts in Mathematics

Applied Linear Algebra is an undergraduate textbook that develops the fundamental ideas and techniques of linear algebra while consistently connecting them to applications in science, engineering, computing, numerical analysis, data analysis, and dynamical systems. Rather than treating linear algebra purely abstractly, Olver and Shakiban emphasize the interaction between theory and practical problems: Gaussian elimination leads naturally to solving linear systems, inner products and orthogonality lead to approximation and least-squares methods, while eigenvalues and singular values provide tools for understanding transformations, stability, data reduction, and dynamical behaviour.

The book progresses from linear systems, vector spaces and bases through inner products, norms, orthogonality, minimization and least squares, before developing more advanced topics such as linear transformations, eigenvalues, singular values, iterative methods and dynamical systems. The second edition expands applications involving numerical methods, signal processing and data analysis while improving the presentation of the theoretical material. Particularly important is the book's effort to explain why linear-algebraic techniques work and when they should be used, rather than presenting them merely as computational algorithms. 

Only single-variable calculus is formally required, and no previous course in linear algebra is assumed, although increasing mathematical maturity is helpful as the material becomes more abstract. It can therefore serve either as a substantial first course in linear algebra or as a more application-oriented second course. Its treatment also provides a strong foundation for later work in differential equations, numerical analysis, statistics and data science. 

Key takeaways

• Strong balance between theoretical linear algebra and real applications.
  
• Covers both classical material—matrices, vector spaces, orthogonality and eigenvalues—and modern topics such as SVD, least squares, iteration, data analysis and dynamical systems. 
  
• Particularly suitable for students interested in applied mathematics, engineering, scientific computing or data science.
  
• More comprehensive than a typical introductory linear-algebra text, reaching naturally toward numerical and applied mathematics.
  

BOOK