Linear algebra: step by step
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2014
|
| Edition: | 1. ed., 1. impr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | VIII, 608 S. Ill., graph. Darst. |
| ISBN: | 9780199654444 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Linear
Equations
and Matrices
1
1.1
Systems of Linear Equations
1
1.2
Gaussian Elimination
12
1.3
Vector Arithmetic
27
1.4
Arithmetic of Matrices
41
1.5
Matrix Algebra
57
1.6
The Transpose and Inverse of a Matrix
75
1.7
Types of Solutions
91
1.8
The Inverse Matrix Method
105
Des Higham
Interview
127
2
Euclidean Space
129
2.1
Properties of Vectors
129
22
Further Properties of Vectors
143
2.3
Linear Independence
159
2.4
Basis and Spanning Set
171
Chao
Yang Interview
190
3
General Vector Spaces
191
3.1
Introduction to
Generai
Vector Spaces
191
3.2
Subspace of a Vector Space
202
3.3
Linear independence and Basis
216
3.4 Dimension 229
3.5
Properties of a Matrix
239
3.6
Linear Systems Revisited
254
Janet Drew Interview
275
4
Inner Product Spaces
277
4.1
Introduction to Inner Product Spaces
277
4.2
Inequalities and Orthogonality
290
4.3
Orthonormai Bases
306
4.4
Orthogonal Matrices
321
Anshul Gupta Interview
338
5
Linear Transformations
339
5-1
Introduction to Linear Transformations
339
5.2
Kernel and Range of a Linear Transformation
352
5.3
Rank and NuHity
364
5.4
Inverse Linear Transformations
372
5-5
The Matrix of a Linear Transformation
389
5.6
Composition and Inverse Linear Transformations
407
Petros Drineas Interview
429
VIU
CONTENTS
6
Determinants and the Inverse Matrix
431
6.1
Determinant of a Matrix
431
6.2
Determinant of Other Matrices
439
6.3
Properties of Determinants
455
6.4
LU
Factorization
472
Françoise Tisseur
Interview
490
7
Eigenvalues and Eigenvectors
491
7.1
Introduction to Eigenvalues and Eigenvectors
491
7.2
Properties of Eigenvalues and Eigenvectors
503
7.3
Diagonalization
518
7.4
Diagonalization of Symmetric Matrices
533
7.5
Singular Value Decomposition
547
Brief Solutions
567
ndex
605
Linear
algebra
is a fundamental area of mathematics, and is arguably the most powerful
mathematical tool ever developed. It is a core topic of study within fields as diverse as: business,
economics, engineering, physics, computer science, ecology, sociology, demography and genetics.
For an example of linear algebra at work, one needs to look no further than the Google search
engine, which relies upon linear algebra to rank the results of a search with respect to relevance.
The strength of the text lies in the large number of examples and the step-by-step explanation
of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit
solutions to set problems freely available online at http://www.oup.co.uk/companion/singh.
The miscellaneous exercises at the end of each chapter are comprised of questions from past
exam papers from various universities, helping to reinforce the reader s confidence. Also included,
generally at the beginning of sections, are short historical biographies of the leading players
in the field of linear algebra to provide context for the topics covered.
The dynamic and engaging style of this book includes frequent question and answer sections
to test the reader s understanding of the methods introduced, rather than encouraging rote learning.
When first encountered, the subject can appear abstract and students will sometimes struggle
to see its relevance; to counter this, the book also contains interviews with key people who use
linear algebra in practice, professionally and academically. It will be an invaluable resource
for undergraduate students in mathematics, the physical sciences and engineering.
Kuldeep Singh is a Senior Lecturer in Mathematics at the University of Hertfordshire.
ALSO PUBLISHED BY
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Matthew
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Cover images Squared Papert. Shutterstockcom/Karramba Production;
Dutch Windmill
2-
Shutterstock.com/JeniFoto: Windmill doodle
L
SrnitterstQCk.corrvAleks Meinik
ISBN
978-0-19-965444-4
OXfORD
UNIVERSITY PRESS
9 r78Öi99 6
www.oup.com
|
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| author | Singh, Kuldeep 1965- |
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| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed., 1. impr. |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:59:36Z |
| institution | BVB |
| isbn | 9780199654444 |
| language | English |
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| physical | VIII, 608 S. Ill., graph. Darst. |
| publishDate | 2014 |
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| spelling | Singh, Kuldeep 1965- Verfasser (DE-588)120600986 aut Linear algebra step by step Kuldeep Singh 1. ed., 1. impr. Oxford Oxford Univ. Press 2014 VIII, 608 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lineare Algebra (DE-588)4035811-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Lineare Algebra (DE-588)4035811-2 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027001649&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027001649&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| subject_GND | (DE-588)4035811-2 (DE-588)4123623-3 |
| title | Linear algebra step by step |
| title_auth | Linear algebra step by step |
| title_exact_search | Linear algebra step by step |
| title_full | Linear algebra step by step Kuldeep Singh |
| title_fullStr | Linear algebra step by step Kuldeep Singh |
| title_full_unstemmed | Linear algebra step by step Kuldeep Singh |
| title_short | Linear algebra |
| title_sort | linear algebra step by step |
| title_sub | step by step |
| topic | Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Lineare Algebra Lehrbuch |
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