Computational and Algorithmic
Linear Algebra and n-Dimensional Geometry

Internet Edition

Katta G. Murty
Dept. of Industrial and Operations Engineering
The University of Michigan, Ann Arbor


This is a sophomore level webbook on linear algebra and n-dimensional geometry with the aim of developing in college entering undergraduates skills in algorithms, computational methods, and mathematical modeling. It is written in a simple style with lots of examples so that students can read most of it on their own. Please see Chapter 0 for the table of contents of the whole book, preface explaining the philosophy of the book and what sets this book apart from other books on linear algebra, and glossary.

Users are encouraged to read most of the book on the computer screen, and print only those portions that they need to look up several times on paper.

Contributions are requested from every user to cover costs, as explained in the preface in Chapter 0.

Many more exercises will be added in each chapter in due course, and weblinks will be installed in the file of each chapter for the user's convenience.

* This book is now published as a regular textbook by World Scientific Publishing Co. (ISBN 978-9814366625) and is currently available in the market. That is why Chapters 1, 3, 4 and the Solutions manual are blocked from public view on this webpage.

Teachers who adopt this book for their classes can get a copy of the Solutions Manual for all the exercises in this book by corresponding with the Publishers
( you can send an e-mail request to Tan Rok Ting, )

Given below is the errata in the first printing (2014) of this book. Corrections may be made at the time of the 2nd printing.

Erratta for "Computational and Algorithmic Linear Algebra and n-Dimensional Geometry"


PAGE Xii, LINE 13: Change "teachers" to "teacher's"


PAGE 1, LINE 5 IN HISTORICAL NOTE: Change "Arabic" to "Persian"
PAGE 7, LINE 10 FROM BOTTOM: Change "subject." to "subject, and Alkhawarizmi is regarded as the Father of Algebra."
PAGE 43, Exercise 1.2.57, LINE 6: Replace "sheaf" with "sheaves"


PAGE 238, LINE 3 in EXAMPLE 3: Change "above" to "below"
PAGE 263, LINE 5: Change "real" to "real valued parameters"
LINE 2 in STEP 2: Change "parameters as" to "parameters βs as"
PAGE 264, LINE 3: Change "real" to "real valued parameters"
PAGE 266, LINE 2 ABOVE EXAMPLE 6: Change "real values." to "real values}."


PAGE 411, LINES 2, 3: Delete "called the geometric multiplicity of the eigen value λ of A."


PAGE 445, LINE 3 FROM BOTTOM: Change "3.16" to "3.20"

Table of Contents

Chapter 0 Contents, Preface, Glossary soph1-0.pdf
Chapter 1 Systems of Simultaneous Linear Equations soph1-1.pdf *
Chapter 2 Matrices, Matrix Arithmetic, Determinants soph1-2.pdf
Chapter 3 n-Dimensional Geometry soph1-3.pdf
Chapter 4 Numerical Linear Algebra soph1-4.pdf *
Chapter 5 Quadratic Forms, Positive, Negative (Semi) Definiteness soph1-5.pdf
Chapter 6 Eigen Values, Eigen Vectors, and Matrix Diagonalization soph1-6.pdf
Chapter 7 Software Systems for Linear Algebra Problems soph1-7.pdf
  Solutions manual for all the exercises LANGsols3.pdf *