Algebra Through Practice: Volume 4, Linear Algebra: A Collection of Problems in Algebra with Solutions

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CUP Archive, Aug 15, 1985 - Mathematics - 116 pages
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Problem-solving is an art central to understanding and ability in mathematics. With this series of books, the authors have provided a selection of worked examples, problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each volume is divided into sections that begin with some notes on notation and prerequisites. The majority of the material is aimed at the students of average ability but some sections contain more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts involved, and practice in the formulation, and so solution, of other problems. Books later in the series cover material at a more advanced level than the earlier titles, although each is, within its own limits, self-contained.
 

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Contents

Duality and normal transformations
18
Solutions to Chapter 1
35
Solutions to Chapter 2
67
Test paper 1
96
Copyright

Common terms and phrases

Algebra bases block Chapter characteristic polynomial choose clearly commute complex Consequently Consider Conversely corresponding Deduce define determine diagonal diagonalisable differentiation dimension distinct dual eigenvalue eigenvectors elements equal equation example exists f relative fact False field F Find Find a Jordan finite finite-dimensional vector space follows geometric multiplicity given gives Hence holds integer invertible matrix isomorphism Jordan basis Jordan normal form Ker f Kert linear functional linear transformation linearly independent LIV,V matrix of f minimum polynomial non-singular non-zero observe obtain orthogonal orthogonal matrix positive definite possible projection Prove quadratic form question relative represented respect result satisfies Show similar similarly solution solve space of dimension spanned squares standard basis subset subspace Suppose symmetric symmetric matrix t-invariant true unique vector space whence zero

About the author (1985)

Greig Beck grew up across the road from Bondi Beach in Sydney, Australia. His early days were spent surfing, sunbaking and reading science fiction on the sand. When he was forced to grow up, he went on to study computer science, and later received an MBA. Greig is the director of a software company but still finds time to write and surf. He lives in Vaucluse, Sydney, with his wife, son and an enormous black German shepherd.

Dark Rising is Greig's second novel.

If you would like to contact Greig Beck, his email address is greig@greigbeck.com and you can find him on the web at www.greigbeck.com

Bibliographic information

QR code for Algebra Through Practice: Volume 4, Linear Algebra
TitleAlgebra Through Practice: Volume 4, Linear Algebra: A Collection of Problems in Algebra with Solutions
Book 4 of Algebra Through Practice, Thomas Scott Blyth a collection of problems in algebra with solutions / T. S. Blyth; E. F. Robertson
Book 4 of Algebra Through Practice: A Collection of Problems in Algebra with Solutions, Thomas Scott Blyth
Online access with purchase: Cambridge Books Online
AuthorsT. S. Blyth, E. F. Robertson
EditorsT. S. Blyth, E. F. Robertson
Editionillustrated
PublisherCUP Archive, 1985
ISBN0521272890, 9780521272896
Length116 pages
Subjects ›  › 

Mathematics / Algebra / General
  
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