This book is an introduction to linear algebra, based on lectures given by the author over 17 years, in the (now defunct) first year course MP103 at the University of Queensland. The style is somewhat formal and terse, in which you won't find any attempt of personification. Definitely a genuine textbook.
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 author's love of discrete things such as integers, rational numbers and finite fields and a distrust of floating point arithmetic.
However, the author has 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.
Both CMAT and the solutions to all problems in the notes are available online.
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