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