Linear Algebra and Its Applications, 2nd Edition 2nd Edition by Lax (PDF)

Description

This set featuresLinear Algebra and Its Applications, Second Edition (978-0-471-75156-4)Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book’s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjoint matrixThe Householder algorithm for turning self-adjoint matrices into tridiagonal formThe compactness of the unit ball as a criterion of finite dimensionality of a normed linear space Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov’s stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy’s elegant proof of Halmos’ conjecture about the numerical range of matrices.Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.and Functional Analysis (978-0-471-55604-6) both by Peter D. Lax.

User’s Reviews

Editorial Reviews: Review “…an informative and useful book, distinguished by its blend of theory and applications, which fulfills its goals admirably.” (MAA Review March 2008) From the Inside Flap Praise for the First Edition”. . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician’s bookshelf.” —American Mathematical MonthlyLinear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book’s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:The QR algorithm for finding the eigenvalues of a self-adjoint matrixThe Householder algorithm for turning self-adjoint matrices into tridiagonal formThe compactness of the unit ball as a criterion of finite dimensionality of a normed linear spaceAdditionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov’s stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy’s elegant proof of Halmos’ conjecture about the numerical range of matrices.Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals. From the Back Cover Praise for the First Edition”. . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician’s bookshelf.” —American Mathematical MonthlyLinear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book’s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:The QR algorithm for finding the eigenvalues of a self-adjoint matrixThe Householder algorithm for turning self-adjoint matrices into tridiagonal formThe compactness of the unit ball as a criterion of finite dimensionality of a normed linear spaceAdditionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov’s stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy’s elegant proof of Halmos’ conjecture about the numerical range of matrices.Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals. About the Author Peter D. Lax, PhD, is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences at New York University. Dr. Lax is the recipient of the Abel Prize for 2005 “for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions”. * A student and then colleague of Richard Courant, Fritz John, and K. O. Friedrichs, he is considered one of the world’s leading mathematicians. He has had a long and distinguished career in pure and applied mathematics, and with over fifty years of experience in the field, he has made significant contributions to various areas of research, including integratable systems, fluid dynamics, and solitonic physics, as well as mathematical and scientific computing. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I would recommend this book to those who have learned linear algebra long ago and plan to pick up some back.This book gives an extremely concise introduction to the core of linear algebra(so not quite the best for beginners), without any redundant sentences in trivial calculation. Starting with linear map and ending in spectral resolution, different parts are united. It also advances with the times, include topics like duality, convexity, which is interesting from engineering perspective.For those who only learn some elementary algebra in undergraduate, this book helps to make a big picture and to show some deep reason behind that.

⭐Great style from a great mind—but a bit too much material.

⭐Good book. Well worked out proofs.

⭐As you can see, the formatting is prohibitive.

⭐Excellent book.

⭐good

⭐Note: The first edition totals 250 pages, ends with Chapter 17, and contains the first eight appendices of the second edition. Here we are offered a first rate exposition by a first class mathematician. An amazing amount of information is packed into this comparatively slim text. Much as a field of nuggets, each step taken points to the direction of another gem. Not easy if one is unaccustomed to the ways and whys of mathematical proofs. However, if allowing for a dose of mathematical maturity, the book does teach and inspire . If the topic of linear algebra seems but a smattering of disconnected entities, then this (non-elementary) textbook might just turn that viewpoint around.(1) First chapter, a rapid-fire snapshot of fundamentals: isomorphisms, linear dependence, equivalence relations.Read: “…this shows forming a quotient space amounts to throwing away information…” (page 6).(2) Linearity and duality: “chapter two might strike the reader–as it does the author– as quintessential tautology.” (page 12). Theorem six, here, quite lovely along with its enlightening proof.(3) Note: application to solutions of Laplace equation. Note: third chapter, exercise seven, presents a beautiful problem (page 24).(4) Matrices, next. Quick and to the point. Following which:(5) Determinants: excellent presentation of concepts and proofs (The Steps: volume,orientation, permutations, Cramer, trace, similarity).(6) Spectral Theory, Eigenvalues: “….analyzes linear maps of a space into itself by decomposing them into their basic constituents.” The proof of Spectral Theorem nicely laid out. That preparation behind us, the next chapter, Euclidean Structure, is painless. Jumping ahead to…(7) calculus (ninth chapter): Theorem four, a delight, as “…the importance of the result lies in the connection it establishes between determinant and trace.” (page 99). Now, jump ahead to page 129– the derivation of the integral relations from theorem fifteen to the last formula (page 132) will prove to be an invaluable adjunct for physicists.(8) The same can be said for the eleventh chapter (an adjunct for physicists) as it deals with kinematics and dynamics. Along with the previous chapter, Matrix Inequalities, this one is a favorite. We read: “The determinant of a positive matrix does not exceed the product of its diagonal elements,” then we delight in proof ! Physicists will delight in that exposition, as interplay of mathematics and physics is displayed to the utmost.(9) Read the pithy statements; these statements are the glue which holds the sections together linguistically.An example: “Convexity is a primitive notion, based on nothing but the bare bones of the structure of linear spaces over the reals…”. Later we encounter normed linear spaces, followed by their linear mappings (chapters 14 and 15).We revel in the presentation of algorithms and limitations on accuracy of solutions: noting a fine section on steepest descent. An appendix details tensor products, beautiful.(10) Concluding: A Review in the American Mathematical Monthly sums it up… “….makes an effort to communicate some of the more unintuitive, but nonetheless important concepts, in Linear Algebra that illustrate the mystery of the dazzling connections between abstract mathematics and the real world.” (Nov. 2001). Finally, these words from Professor Lax: “It is instructive to recall that in the 1940’s Linear Algebra was dead as a subject for research, it was ready to be entombed in textbooks.”Thankfully, we have texts such as this which propel one (and prepare one) for further research.Whether your interests are pure or applied, mathematics or physics, this exposition is as delightful as any to peruse.Challenging, but, not too much so. In other words, accessible.Highly Recommended !

⭐After reading it, I became to realize that I know nothing about linear algebra. My intuition clearly tells that this is an excellent book, but the only problem is that I can not fully understand it. Sometimes the author diverges a little bit, maybe not just a little bit, the reader should always keep in mind that the main line is the first 8 chapters. If you find that you can not continue reading anymore, it is a good time to review the first 8 chapters again.

⭐It was a very good bargain.

⭐good

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