LECTURE NOTES OF WILLIAM CHEN

 

LINEAR ALGEBRA

This set of notes has been compiled over a period of more than 30 years. Some chapters were used in various forms and on many occasions between 1981 and 1990 by the author at Imperial College, University of London. The remaining chapters were written in Sydney.

The material has been organized in such a way to create a single volume suitable to take the reader to a reasonable level of linear algebra. Chapters 1 - 4 cover very basic material. The concept of vector spaces is then introduced in Chapters 5 - 7. More advanced topics, including the concept of linear transformations from one vector space to another and the concept of inner products, are covered in Chapters 8 - 12.

To read the notes, click the links below for connection to the appropriate PDF files.

The material is available free to all individuals, on the understanding that it is not to be used for financial gain, and may be downloaded and/or photocopied, with or without permission from the author. However, the documents may not be kept on any information storage and retrieval system without permission from the author, unless such system is not accessible to any individuals other than its owners.

SECTION A --- ELEMENTARY TOPICS

Chapter 1 : LINEAR EQUATIONS >>

Chapter 2 : MATRICES >>

Chapter 3 : DETERMINANTS >>

Chapter 4 : VECTORS >>

SECTION B --- INTRODUCTION TO SOME ALGEBRAIC STRUCTURES

Chapter 5 : INTRODUCTION TO VECTOR SPACES >>

Chapter 6 : VECTOR SPACES ASSOCIATED WITH MATRICES >>

Chapter 7 : EIGENVALUES AND EIGENVECTORS >>

SECTION C --- FURTHER TOPICS

Chapter 8 : LINEAR TRANSFORMATIONS >>

Chapter 9 : REAL INNER PRODUCT SPACES >>

Chapter 10 : ORTHOGONAL MATRICES >>

Chapter 11 : APPLICATIONS OF REAL INNER PRODUCT SPACES >>

Chapter 12 : COMPLEX VECTOR SPACES >>