Advanced linear and matrix algebra / Nathaniel Johnston.
Johnston, Nathaniel, author.
2021
QA184.2 .J64 2021
Available Online

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Title Advanced linear and matrix algebra / Nathaniel Johnston.
Author Johnston, Nathaniel, author.
ISBN 9783030528157 (electronic bk.)
3030528154 (electronic bk.)
9783030528164 (print)
3030528162
9783030528171 (print)
3030528170
9783030528140
3030528146
DOI https://doi.org/10.1007/978-3-030-52815-7
Published Cham : Springer, [2021]
Copyright ©2021
Language English
Description 1 online resource : illustrations (chiefly color)
Item Number 10.1007/978-3-030-52815-7 doi
Call Number QA184.2 .J64 2021
Dewey Decimal Classification 512/.5
Summary 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.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 9, 2021).
Available in Other Form Print version: 9783030528140
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Chapter 1: Vector Spaces
Chapter 2: Matrix Decompositions
Chapter 3: Tensors and Multilinearity
Appendix A: Mathematical Preliminaries
Appendix B: Additional Proofs
Appendix C: Selected Exercise Solutions.

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