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Advanced Linear and Matrix Algebra

Authors: Johnston, Nathaniel

  • Motivates a deeper understanding of the abstract structures needed to tackle questions in mathematics, data analysis, and quantum information theory
  • Engages readers with a visual approach that uses color to enhance both content and learning
  • Features a wide selection of theoretical and applied topics to complement the core material
  • Incorporates exercises of all levels
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Buy this book

eBook $54.99
price for USA in USD
  • The eBook version of this title will be available soon
  • Due: March 11, 2021
  • ISBN 978-3-030-52815-7
  • Digitally watermarked, DRM-free
  • Included format:
  • Immediate eBook download after purchase and usable on all devices
Hardcover $69.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: February 11, 2021
  • ISBN 978-3-030-52814-0
  • Free shipping for individuals worldwide. Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering
  • Usually ready to be dispatched within 3 to 5 business days
About this Textbook

This textbook emphasizes the interplay between algebra and geometry to motivate the study of advanced linear algebra techniques. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. Building on a first course in linear algebra, this book offers readers a deeper understanding of abstract structures, matrix decompositions, multilinearity, and tensors. Concepts draw on concrete examples throughout, offering accessible pathways to advanced techniques.

Beginning with a study of vector spaces that includes coordinates, isomorphisms, orthogonality, and projections, the book goes on to focus on matrix decompositions. Numerous decompositions are explored, including the Shur, spectral, singular value, and Jordan decompositions. In each case, the author ties the new technique back to familiar ones, to create a coherent set of tools. Tensors and multilinearity complete the book, with a study of the Kronecker product, multilinear transformations, and tensor products. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from the QR and Cholesky decompositions, to matrix-valued linear maps and semidefinite programming. Exercises of all levels accompany each section.

Advanced Linear and Matrix Algebra offers students of mathematics, data analysis, and beyond the essential tools and concepts needed for further study. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. A first course in proof-based linear algebra is assumed. An ideal preparation can be found in the author’s companion volume, Introduction to Linear and Matrix Algebra.


About the authors

Nathaniel Johnston is an Associate Professor of Mathematics at Mount Allison University in New Brunswick, Canada. His research makes use of linear algebra, matrix analysis, and convex optimization to tackle questions related to the theory of quantum entanglement. His companion volume, Introduction to Linear and Matrix Algebra, is also published by Springer.

Buy this book

eBook $54.99
price for USA in USD
  • The eBook version of this title will be available soon
  • Due: March 11, 2021
  • ISBN 978-3-030-52815-7
  • Digitally watermarked, DRM-free
  • Included format:
  • Immediate eBook download after purchase and usable on all devices
Hardcover $69.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: February 11, 2021
  • ISBN 978-3-030-52814-0
  • Free shipping for individuals worldwide. Please be advised Covid-19 shipping restrictions apply. Please review prior to ordering
  • Usually ready to be dispatched within 3 to 5 business days
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Bibliographic Information

Bibliographic Information
Book Title
Advanced Linear and Matrix Algebra
Authors
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-52815-7
DOI
10.1007/978-3-030-52815-7
Hardcover ISBN
978-3-030-52814-0
Edition Number
1
Number of Pages
XIII, 497
Number of Illustrations
5 b/w illustrations, 100 illustrations in colour
Topics