Practical linear algebra : a geometry toolbox
著者
書誌事項
Practical linear algebra : a geometry toolbox
（An A K Peters book）
CRC Press, Taylor & Francis Group, c2014
3rd ed
- : hardback
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注記
Includes bibliographical references (p. 487-488) and index
内容説明・目次
内容説明
Through many examples and real-world applications, Practical Linear Algebra: A Geometry Toolbox, Third Edition teaches undergraduate-level linear algebra in a comprehensive, geometric, and algorithmic way. Designed for a one-semester linear algebra course at the undergraduate level, the book gives instructors the option of tailoring the course for the primary interests: math, engineering, science, computer graphics, and geometric modeling.
New to the Third Edition
More exercises and applications
Coverage of singular value decomposition and its application to the pseudoinverse, principal components analysis, and image compression
More attention to eigen-analysis, including eigenfunctions and the Google matrix
Greater emphasis on orthogonal projections and matrix decompositions, which are tied to repeated themes such as the concept of least squares
To help students better visualize and understand the material, the authors introduce the fundamental concepts of linear algebra first in a two-dimensional setting and then revisit these concepts and others in a three-dimensional setting. They also discuss higher dimensions in various real-life applications. Triangles, polygons, conics, and curves are introduced as central applications of linear algebra.
Instead of using the standard theorem-proof approach, the text presents many examples and instructional illustrations to help students develop a robust, intuitive understanding of the underlying concepts. The authors' website also offers the illustrations for download and includes Mathematica (R) code and other ancillary materials.
目次
Descartes' Discovery. Here and There: Points and Vectors in 2D. Lining Up: 2D Lines. Changing Shapes: Linear Maps in 2D. 2 x 2 Linear Systems. Moving Things Around: Affine Maps in 2D. Eigen Things. 3D Geometry. Linear Maps in 3D. Affine Maps in 3D. Interactions in 3D. Gauss for Linear Systems. Alternative System Solvers. General Linear Spaces. Eigen Things Revisited. The Singular Value Decomposition. Breaking It Up: Triangles. Putting Lines Together: Polylines and Polygons. Conics. Curves. Appendices. Bibliography. Index.
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