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Further Linear Algebra de T. S. Blyth

Further Linear Algebra: Springer Undergraduate Mathematics Series

Autor T. S. Blyth, E F. Robertson
en Limba Engleză Paperback – 5 oct 2001

În cadrul programului de studii universitare de licență, tranziția de la conceptele elementare de calcul matriceal la structurile abstracte ale algebrei liniare reprezintă un punct critic. Further Linear Algebra este concepută special pentru a facilita această trecere, fiind poziționată ca o continuare naturală a volumului Basic Linear Algebra. Dacă primul volum se concentra pe spații vectoriale finit dimensionale și diagonalizarea matricelor, acest text extinde cadrul propus de Basic Linear Algebra cu date noi din sfera proprietăților avansate ale mapping-urilor liniare și structurilor vectoriale complexe.

Observăm în această lucrare o metodologie didactică riguroasă, specifică autorilor T. S. Blyth și E F. Robertson. Aceștia păstrează viziunea din Sets and Mappings, unde algebra este tratată ca un etalon al raționamentului matematic pur, dar aplică aici o structură pragmatică, similară celei din Algebra Through Practice: Volume 4, Linear Algebra. Cartea progresează logic de la spații cu produs intern și sume directe către teme de profunzime precum descompunerea primară, reducerea la forma Jordan și studiul spațiilor duale.

Un element distinctiv față de alte cursuri teoretice, cum este cel al lui Serge Lang, îl reprezintă capitolul dedicat utilizării MAPLE. Într-o manieră similară cu Principles of Linear Algebra With Maple, autorii recunosc necesitatea instrumentelor computaționale în gestionarea calculelor laborioase, oferind un tutorial accesibil pentru integrarea software-ului în rezolvarea problemelor algebrice. Textul nu se limitează la teorie, ci include numeroase exemple lucrate și exerciții cu soluții incluse, facilitând studiul individual.

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Specificații

ISBN-13: 9781852334253
ISBN-10: 1852334258
Pagini: 244
Ilustrații: VII, 230 p. 2 illus.
Dimensiuni: 178 x 235 x 14 mm
Greutate: 0.43 kg
Ediția:2002
Editura: Springer
Colecția Springer Undergraduate Mathematics Series
Seria Springer Undergraduate Mathematics Series

Locul publicării:London, United Kingdom

Public țintă

Lower undergraduate

De ce să citești această carte

Recomandăm această carte studenților de la facultățile de matematică și informatică care doresc să stăpânească algebra liniară dincolo de nivelul introductiv. Cititorul câștigă o înțelegere profundă a formelor canonice și a dualității, beneficiind în același timp de un ghid practic pentru utilizarea MAPLE. Este o resursă esențială pentru pregătirea examenelor avansate, oferind rigoarea editurii Springer într-un format accesibil.

Descriere scurtă

Most of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the exercises are also provided. Many applications of linear algebra require careful, and at times rather tedious, calculations by hand. Very often these are subject to error, so the assistance of a com­ puter is welcome. As far as computation in algebra is concerned, there are several packages available. Here we include, in the spirit of a tutorial, a chapter that gives 1 a brief introduction to the use of MAPLE in dealing with numerical and algebraic problems in linear algebra.

Cuprins

The story so far.- 1. Inner Product Spaces.- 2. Direct Sums of Subspaces.- 3. Primary Decomposition.- 4. Reduction to Triangular Form.- 5. Reduction to Jordan Form.- 6. Rational and Classical Forms.- 7. Dual Spaces.- 8. Orthogonal Direct Sums.- 9. Bilinear and Quadratic Forms.- 10. Real Normality.- 11. Computer Assistance.- 12. …. but who were they?.- 13. Solutions to the Exercises.

Recenzii

From the reviews of the first edition:
MAA ONLINE
"This book will be of interest to anyone who wishes to have a good grasp of linear llgebra and matrix theory. It can also be used as an advanced undergraduate textbook. Although this book does not treat infinite dimensional linear spaces, it provides the reader with a deep understanding of finite dimensional linear spaces. Many aspects of the theory of finite dimensional linear spaces can easily be generalized to the infinite dimensional case. Therefore, this book will also be helpful to those who intend to study infinite dimensional spaces later. "
ZENTRALBLATT MATH
"…it embodies a beautiful, concise and precise treatment of the subject, with succinct numerical and algebraic worked examples at the right points, and many exercises…This is an excellent textbook which, together with the earlier book, comprises a very nearly complete introduction to linear algebra which not only the undergraduate but also the advanced reader will enjoy studying."
"The present book is a contribution of the volume Basic Linear Algebra of the same authors, which appeared in the same Springer series. … It is a very interesting, accessible book for undergraduates (or teacher professors), and the many examples and exercises should really help the undergraduate to study its contents." (Koen Thas, Bulletin of the Belgian Mathematical Society, Vol. 11 (4), 2004)
"The book is a contribution of the authors’ Basic Linear Algebra published in the same series. … Besides numerous well-chosen examples scattered throughout the text, the reader can also enjoy short biographical profiles of twenty one eminent mathematicians associated with the subject." (European Mathematical Society Newsletter, December, 2003)
"The present book is a natural sequel to the same authors’ successful SUMS volume ‘Basic Linear Algebra’. The most advanced topics here take the reader to the veryheart of the subject … . To sum up, this textbook is well suited for self-study or for a one- or two-semester course. Therefore, we warmly recommend it to undergraduate students studying as well as professors teaching Linear Algebra at any level." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 69, 2003)
"Further Linear Algebra is a natural sequel to the authors’ highly acclaimed SUMS volume Basis Linear Algebra. … An introductory chapter recaps the prerequisites (for those readers unfamiliar with the first volume), and a wide range of worked examples and exercises (with solutions) are strategically placed throughout the text to consolidate understanding." (L’Enseignement Mathematique, Vol. 48 (1-2), 2002)

Caracteristici

Follows on from "Basic Linear Algebra", one of SUMS' best-selling titles, to provide a textbook suitable for a second course in linear algebra Includes a wealth of worked examples and exercises Includes a brief introduction, in the style of a tutorial, to the use of MAPLE in dealing with numerical and algebraic problems