Linear Algebra I

Synopsis

A rigorous first course in linear algebra. The ideas introduced previously for 2- and 3-dimensional space are developed and extended in a more general setting. Definitions and examples of fields and vector spaces. Subspaces, spanning sets, linear independence, bases, dimension, direct sums. Linear mappings, kernel and image. Matrices and matrix algebra. Determinants. Echelon form. Eigenvectors and diagonalization. Orthogonal diagonalization of a real symmetric matrix.

Lecture notes etc.

My most recent lecture notes for this module are from 2005. I wrote them as Maple worksheets and then printed them as PDF files, which are available below. The chapters are available separately as the files "Chapter 0" to "Chapter 11", or together as the single (large) file "All Chapters." I also produced an animation to illustrate eigenvectors using Maple and saved it as a GIF file, which is mentioned in Chapter 10 and available below.

Further reading

I make no specific reference to any text book in my lecture notes, but it can be very useful to have a text book for reference purposes and to provide a "second opinion". The main text book that I used, which I recommend, is Linear Algebra by Seymour Lipshutz, Schaum Outline Series (ISBN: 0071362002). It normally costs about £10, although amazon may sell it (considerably) cheaper! Other text books may be equally suitable. Beware that text books may use different definitions from mine.

Lecture notes by Professor Peter Cameron for the follow-on module, Linear Algebra II, are also still available.