The Less Is More Linear Algebra Of Vector Spaces And Matrices

Author : Daniela Calvetti
Publisher : SIAM
ISBN 13 : 1611977401
Total Pages : 181 pages
Book Rating : 4.00/5 ( download)

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Download or read book The Less Is More Linear Algebra of Vector Spaces and Matrices written by Daniela Calvetti and published by SIAM. This book was released on 2022-11-30 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 that 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.

Author : Robert M. Thrall
Publisher : Courier Corporation
ISBN 13 : 0486321053
Total Pages : 336 pages
Book Rating : 4.59/5 ( download)

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Download or read book Vector Spaces and Matrices written by Robert M. Thrall and published by Courier Corporation. This book was released on 2014-01-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.

Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 410 pages
Book Rating : 4.80/5 ( download)

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Download or read book Groups, Matrices, and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

Author : Lawrence P. Huelsman
Publisher : Courier Corporation
ISBN 13 : 0486280446
Total Pages : 304 pages
Book Rating : 4.48/5 ( download)

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Download or read book Circuits, Matrices and Linear Vector Spaces written by Lawrence P. Huelsman and published by Courier Corporation. This book was released on 2013-08-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, the basic theory of n-dimensional spaces, and applications to linear systems. Numerous problems. 1963 edition.

Author : Melvin Hausner
Publisher : Courier Dover Publications
ISBN 13 : 0486835391
Total Pages : 417 pages
Book Rating : 4.96/5 ( download)

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Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.

Author : Hans Schneider
Publisher : Courier Corporation
ISBN 13 : 0486139301
Total Pages : 430 pages
Book Rating : 4.02/5 ( download)

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Download or read book Matrices and Linear Algebra written by Hans Schneider and published by Courier Corporation. This book was released on 2012-06-08 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it. This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations. Table of Contents: l. The Algebra of Matrices 2. Linear Equations 3. Vector Spaces 4. Determinants 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Inner Product Spaces 8. Applications to Differential Equations For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.

Author : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.60/5 ( download)

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Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Author : Alan Tucker
Publisher : Macmillan College
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.45/5 ( download)

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Download or read book Linear Algebra written by Alan Tucker and published by Macmillan College. This book was released on 1993 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the fundamental role of linear algebra with both pure and applied mathematics as well as client disciplines such as engineering, the physical sciences and economics. This text examines the interrelationships amongst theory, computation and applications.

Author : William Brown
Publisher : CRC Press
ISBN 13 : 9780824784195
Total Pages : 338 pages
Book Rating : 4.97/5 ( download)

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Download or read book Matrices and Vector SPates written by William Brown and published by CRC Press. This book was released on 1991-03-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for a one-semester course in linear algebra for graduate or upper-level undergraduate students of mathematics and engineering. Employs a matrix perspective, and emphasizes training in definitions, theorems, and proofs. Annotation copyright Book News, Inc. Portland, Or.

Author : Shmuel Friedland
Publisher : SIAM
ISBN 13 : 1611975131
Total Pages : 301 pages
Book Rating : 4.30/5 ( download)

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Download or read book Linear Algebra and Matrices written by Shmuel Friedland and published by SIAM. This book was released on 2018-01-30 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as constructive discussions about the motivation of fundamental concepts, many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks.The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics. The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest.