MARC details
| 000 -LEADER |
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| fixed length control field |
04119nam a2200373 4500 |
| 001 - CONTROL NUMBER |
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| control field |
OTLid0000188 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
MnU |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20201105133302.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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| fixed length control field |
m o d s |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
180907s2016 mnu o 0 0 eng d |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
MnU |
| Language of cataloging |
eng |
| Transcribing agency |
MnU |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA1 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA37.3 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Cherney, David |
| Relator term |
author |
| 245 00 - TITLE STATEMENT |
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| Title |
Linear Algebra |
| Statement of responsibility, etc. |
David Cherney |
| 264 #2 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Name of producer, publisher, distributor, manufacturer |
Open Textbook Library |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Name of producer, publisher, distributor, manufacturer |
University of California, Davis |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
1 online resource |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Open textbook library. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1 What is Linear Algebra? -- 2 Systems of Linear Equations -- 3 The Simplex Method -- 4 Vectors in Space, n-Vectors -- 5 Vector Spaces -- 6 Linear Transformations -- 7 Matrices -- 8 Determinants -- 9 Subspaces and Spanning Sets -- 10 Linear Independence -- 11 Basis and Dimension -- 12 Eigenvalues and Eigenvectors -- 13 Diagonalization -- 14 Orthonormal Bases and Complements -- 15 Diagonalizing Symmetric Matrices -- 16 Kernel, Range, Nullity, Rank -- 17 Least squares and Singular Values |
| 520 0# - SUMMARY, ETC. |
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| Summary, etc. |
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an "exploration chapter" on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late, since we prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications-least squares and singular values. These are a fun way to end any lecture course. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems. |
| 542 1# - INFORMATION RELATING TO COPYRIGHT STATUS |
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| Copyright statement |
Attribution-NonCommercial-ShareAlike |
| 546 ## - LANGUAGE NOTE |
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| Language note |
In English. |
| 588 0# - SOURCE OF DESCRIPTION NOTE |
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| Source of description note |
Description based on online resource |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics |
| Form subdivision |
Textbooks |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Denton, Tom |
| Relator term |
author |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Waldon, Andrew K. |
| Relator term |
author |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
Open Textbook Library |
| Relator term |
distributor |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://open.umn.edu/opentextbooks/textbooks/188">https://open.umn.edu/opentextbooks/textbooks/188</a> |
| Public note |
Access online version |
