The less is more linear algebra of vector spaces and matrices

Author(s)

Bibliographic Information

The less is more linear algebra of vector spaces and matrices

Daniela Calvetti, Erkki Somersalo

(OT, 187)

Society for Industrial and Applied Mathematics, c2023

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Description and Table of Contents

Description

Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)-arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.

by "Nielsen BookData"

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    Society for Industrial and Applied Mathematics

Details

  • NCID
    BD02367996
  • ISBN
    • 9781611977394
  • LCCN
    2022948985
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Philadelphia
  • Pages/Volumes
    xii, 168 p.
  • Size
    26 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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