Practical Linear Algebra (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
514
Utgivningsdatum
2013-08-19
Upplaga
3 New edition
Förlag
A K Peters
Illustratör/Fotograf
492 black & white illustrations
Illustrationer
320; 492 Illustrations, black and white
Dimensioner
234 x 196 x 25 mm
Vikt
1065 g
Antal komponenter
1
ISBN
9781466579569
Practical Linear Algebra (inbunden)

Practical Linear Algebra

A Geometry Toolbox, Third Edition

Inbunden Engelska, 2013-08-19
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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.
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Praise for the Second Edition: "... quite appropriate for students in engineering and computer graphics as well as in mathematics. It is well written and the examples are carefully chosen to motivate or exemplify the topic at hand. ... Recommended." -J.R. Burke, CHOICE, September 2005 "I picked up this book with the thought, 'oh, another linear algebra text.' I was pleasantly surprised, upon examination, that it is not just another one. The standard linear algebra material is presented with good motivating stories, illustrations, and examples." -CMS Notes, February 2006 "[The] mixture of linear algebra, geometry, and numerical aspects is very interesting and will probably stimulate the students." -Bulletin of the Belgian Mathematical Society, December 2005 "Teaching computer graphics and mathematics in the study program Digital Media, I have found Practical Linear Algebra to be precisely the kind of book I've long been looking for. It covers all topics that are vital for computer graphics, even gives lots of applications in that field, including for instance PostScript, and does so in a very practical but nonetheless rigorous manner. I find many elements of my own teaching in this book, including the hand-made style of drawings (rendering them more 'hands-on'), using a geometric shape to illustrate the action of a 2x2 matrix, and deriving the determinant from the computation of areas and volumes instead of plainly presenting a formula. I have recommended this book strongly to all students in my first-year courses and will continue to do so." -Joern Loviscach, University of Applied Sciences Bremen "I was impressed with the applications, especially those related to computer graphics. ... I think some faculty will be interested in using the book because the geometric descriptions and applications are very nice." -Linda Patton, Cal Poly San Luis Obispo "I just purchased your book ... and I immediately fell in love with it. I love the nice illustrations and diagrams, which are very helpful in promoting an intuitive understanding of every concept. I am a clinician investigator at the National Institutes of Health who is conducting MRI research of the heart. My main interest is finite deformation of the heart muscle structures; however, since I do not have an engineering background, I have been looking for a nice textbook on linear algebra." -Hiroshi Ashikaga, National Institutes of Health "After having finished your book today, I agree completely with the very favorable reviews that I saw on the Internet. It was an enlightening experience to brush up on my old university math with this book. The 'sketchy' way of explaining things sure worked for me." -Anneke Sicherer-Roetman, Maritime Research Institute Netherlands "... it's done a world of wonder for me, as I need to review my linear algebra to prepare for studying computer graphics. I really can't thank you enough." -Daniel Kurtz, Northeastern University "Practical Linear Algebra is great. I write software for the image analysis of medical images where in several occasions I have had to deal with eigen things and [others]. I have been using your book as a valuable reference to refresh and understand these concepts that I studied when I was a student." -Diego Bordegari

Bloggat om Practical Linear Algebra

Innehållsförteckning

Descartes' Discovery Local and Global Coordinates: 2D Going from Global to Local Local and Global Coordinates: 3D Stepping Outside the Box Application: Creating Coordinates Here and There: Points and Vectors in 2D Points and Vectors What's the Difference? Vector Fields Length of a Vector Combining Points Independence Dot Product Orthogonal Projections Inequalities Lining Up: 2D Lines Defining a Line Parametric Equation of a Line Implicit Equation of a Line Explicit Equation of a Line Converting Between Parametric and Implicit Equations Distance of a Point to a Line The Foot of a Point A Meeting Place: Computing Intersections Changing Shapes: Linear Maps in 2D Skew Target Boxes The Matrix Form Linear Spaces Scalings Reflections Rotations Shears Projections Areas and Linear Maps: Determinants Composing Linear Maps More on Matrix Multiplication Matrix Arithmetic Rules 2 x 2 Linear Systems Skew Target Boxes Revisited The Matrix Form A Direct Approach: Cramer's Rule Gauss Elimination Pivoting Unsolvable Systems Underdetermined Systems Homogeneous Systems Undoing Maps: Inverse Matrices Defining a Map A Dual View Moving Things Around: Affine Maps in 2D Coordinate Transformations Affine and Linear Maps Translations More General Affine Maps Mapping Triangles to Triangles Composing Affine Maps Eigen Things Fixed Directions Eigenvalues Eigenvectors Striving for More Generality The Geometry of Symmetric Matrices Quadratic Forms Repeating Maps 3D Geometry From 2D to 3D Cross Product Lines Planes Scalar Triple Product Application: Lighting and Shading Linear Maps in 3D Matrices and Linear Maps Linear Spaces Scalings Reflections Shears Rotations Projections Volumes and Linear Maps: Determinants Combining Linear Maps Inverse Matrices More on Matrices Affine Maps in 3D Affine Maps Translations Mapping Tetrahedra Parallel Projections Homogeneous Coordinates and Perspective Maps Interactions in 3D Distance between a Point and a Plane Distance between Two Lines Lines and Planes: Intersections Intersecting a Triangle and a Line Reflections Intersecting Three Planes Intersecting Two Planes Creating Orthonormal Coordinate Systems Gauss for Linear Systems The Problem The Solution via Gauss Elimination Homogeneous Linear Systems Inverse Matrices LU Decomposition Determinants Least Squares Application: Fitting Data to a Femoral Head Alternative System Solvers The Householder Method Vector Norms Matrix Norms The Condition Number Vector Sequences Iterative System Solvers: Gauss-Jacobi and Gauss-Seidel General Linear Spaces Basic Properties of Linear Spaces Linear Maps Inner Products Gram-Schmidt Orthonormalization A Gallery of Spaces Eigen Things Revisited The Basics Revisited The Power Method Application: Google Eigenvector Eigenfunctions The Singular Value Decomposition The Geometry of the 2 x 2 Case The General Case SVD Steps Singular Values and Volumes The Pseudoinverse Least Squares Application: Image Compression Principal Components Analysis Breaking It Up: Triangles Barycentric Coordinates Affine Invariance Some Special Points 2D Triangulations A Data Structure Application: Point Location 3D Triangulations Putting Lines Together: Polylines and Polygons Polylines Polygons Convexity Types of Polygons Unusual Polygons Turning Angles and Winding Numbers Area Application: Planarity Test Application: Inside or Outside? Conics The General Conic Analyzing Conics General Conic to Standard Position Curves Parametric Curves Properties of Bezier Curves The Matrix Form Derivatives Composite Curves The Geometry of Planar Curves Moving along a Curve Appendix A: Glossary Appendix B: Selected Exercise Solutions Bibliography Index Exercises appear at the end of each chapter.