### Preface

This book is an introduction to linear algebra, based on lectures given
by me over 17 years, in the (now defunct) first year course MP103 at the
University of Queensland.

The style is somewhat formal and terse, whereas in the lecture room I like to
open up and present even the most boring things with enthusiasm and motivation.
The book *Linear Algebra, an introduction with concurrent examples*, by A.G. Hamilton, CUP 1989, is on a similar level, with much more emphasis on good pedagogy.

In the first edition I included a chapter on the LDU algorithm. However I
omitted this from the second edition and instead recommend the reader to
either C.G. Cullen, *Linear Algebra with Applications* or I.N. Herstein and D.J. Winter, *A Primer of Linear Algebra*, Macmillan 1988.

Students are encouraged to try the problems, which range from the mechanical
to the more subtle, the latter demanding a greater level of interaction from
the student.

The section on subspaces is meant to be a gentle introduction to the second
course, where abstract vector spaces are met in detail. Things of substance are
met here, including the rank of a matrix.

The section on three dimensional geometry makes use of the earlier sections
on linear equations, matrices and determinants and some of the proofs are more
algebraic (even pedantic) than some readers would like.

One criticism of the book has been its neglect of the computational side of the
subject. This is partly a reflection of my love of discrete things such as
integers, rational numbers and finite fields and a distrust of floating point
arithmetic.

However, one redeeming feature is that I have written an exact arithmetic matrix program called
CMAT, which performs exact calculations on
matices whose elements are rational numbers, complex rational numbers or
numbers from a finite field of p (prime) elements. CMAT takes the hard work out
of calculating things such as the reduced row echelon form, the determinant and
characteristic polynomial of a matrix.

Peter Adams produced the conics diagrams in Chapter 7 with his excellent
CONICS program. Unfortunately this is not available in CMAT, as CONICS was
written with specific graphics commands relevant to a special type of terminal!

I have also made the solutions to all problems in the notes available on
the WWW.

The notes are freely available for educational purposes and are not to be used
for monetary gain.

* Last modified 8th August 2005*