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Linear Algebra Concepts and Techniques On Euclidean Spaces: Ma siu Lun
This publication is the successor of the third edition of the book "Linear
Algebra I" published by the authors with their previous publisher. It is used
as the course lecture notes for the undergraduate module MA1101R, Linear
Algebra I, offered by the Department of Mathematics at the National Univer-
sity of Singapore. This module is the first course on linear algebra and it serves
as an introduction to the basic concepts of linear algebra that are routinely
applied in diverse fields such as science, engineering, statistics, economics and
computing. Mindful that majority of the students taking this module are new
to the subject, we have chosen to introduce the concepts of linear algebra in the
context of Euclidean spaces rather than to jump straight into abstract vector
spaces, which will be covered in the second course. The set up in Euclidean
spaces also facilitates the connections between the algebraic and geometric
viewpoints of linear algebra.
Formal proofs of most of the basic theorems in linear algebra have been in-
cluded to enhance a proper understanding of the fundamental ideas and tech-
niques. Several applications of linear algebra in some of the fields mentioned
above are also highlighted. At the end of every chapter is a good collection of
problems, all of which are culled from tutorial problems, test and examination
questions from the same module taught by the authors in the past. These
problems range from the straightforward computational ones to some highly
challenging questions. In order to achieve a deeper understanding of the topic,
students are advised to work through these problems.
Significant updates and revisions have been made in this new edition, in-
cluding the discussion, examples and exercises. Many of the changes are done
in response to feedback received from students, and teaching after-thoughts
that the authors have accumulated over the past years. We believe that the revisions made to the presentation of materials will further enhance learners'
understanding of the critical concepts in this subject.
Finally, the authors would like to thank their colleagues from the Mathe-
matics Department in NUS who have contributed to the very first version of
the lecture notes in 1998, especially Chan Onn, Tan Hwee Huat, Roger Tan
Choon Ee and Tang Wai Shing. More recently, Toh Pee Choon (now with
the National Institute of Education) has also given many useful comments on
areas of improvement from the previous edition.
Algebra I" published by the authors with their previous publisher. It is used
as the course lecture notes for the undergraduate module MA1101R, Linear
Algebra I, offered by the Department of Mathematics at the National Univer-
sity of Singapore. This module is the first course on linear algebra and it serves
as an introduction to the basic concepts of linear algebra that are routinely
applied in diverse fields such as science, engineering, statistics, economics and
computing. Mindful that majority of the students taking this module are new
to the subject, we have chosen to introduce the concepts of linear algebra in the
context of Euclidean spaces rather than to jump straight into abstract vector
spaces, which will be covered in the second course. The set up in Euclidean
spaces also facilitates the connections between the algebraic and geometric
viewpoints of linear algebra.
Formal proofs of most of the basic theorems in linear algebra have been in-
cluded to enhance a proper understanding of the fundamental ideas and tech-
niques. Several applications of linear algebra in some of the fields mentioned
above are also highlighted. At the end of every chapter is a good collection of
problems, all of which are culled from tutorial problems, test and examination
questions from the same module taught by the authors in the past. These
problems range from the straightforward computational ones to some highly
challenging questions. In order to achieve a deeper understanding of the topic,
students are advised to work through these problems.
Significant updates and revisions have been made in this new edition, in-
cluding the discussion, examples and exercises. Many of the changes are done
in response to feedback received from students, and teaching after-thoughts
that the authors have accumulated over the past years. We believe that the revisions made to the presentation of materials will further enhance learners'
understanding of the critical concepts in this subject.
Finally, the authors would like to thank their colleagues from the Mathe-
matics Department in NUS who have contributed to the very first version of
the lecture notes in 1998, especially Chan Onn, Tan Hwee Huat, Roger Tan
Choon Ee and Tang Wai Shing. More recently, Toh Pee Choon (now with
the National Institute of Education) has also given many useful comments on
areas of improvement from the previous edition.
257 pages, Kindle Edition
Published March 9, 2018
2 people want to read
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