- Handouts; Lecture notes; Problems/Solutions
- The Course Outline
- Some Reference books
- The 1991 MP274 notes (These contain extra reading for interested honours students)
- The final 1999 exam
- Some Study Suggestions
- Understanding Mathematics (University of Utah - Peter Alfeld)
- Coping With Math Anxiety (B. Sidney Smith and Wendy Hageman Smith)
- On the Centrality of Linear Algebra in the Curriculum, by Carl C. Cowen
*Matrix Analysis and Applied Linear Algebra*, (Online version of a textbook by Carl D. Meyer)*Resources for teaching linear algebra*, D. Carlson et al. (A collection of viewpoints on student difficulties in understanding linear algebra)- Factoris, an online calculator by Xiao Gang

We study reduced row echelon form of matrices, vector spaces, coordinates & change of basis, linear transformations, eigenvalues, canonical forms for matrices, inner product spaces.

The subject contains many interesting algorithms. Students can experiment with an exact arithmetic matrix computer program called **CMAT**, written by the lecturer and which implements some of the algorithms met with in the course.

The program can also be downloaded.

*Elementary Linear Algebra*, H. Anton, QA184.A571984*Linear Algebra and Applications*, C. Cullen, QA184. C851988*Linear Algebra*, C.W. Curtis, QA184.C871984*Linear Algebra*, S.H. Friedberg, A.J. Insel, L.E. Spence, QA184.F81989*Elementary Linear Algebra*, R.E. Larson and B.H. Edwards, QA184.L391991*Linear Algebra with applications*, Steven Leon, QA184 .L46 1998*Linear Algebra*, S. Lipschutz, QA251.L531991*Linear Algebra*, M. O'Nan, QA184.O51976*Linear Algebra*, L. Smith, QA184.S6319781*Matrix theory and linear algebra*, I.N. Herstein, David J. Winter, QA188 .H47 1988

### Various handouts

- k-termed linear recurrences (html file) (Handed out 17th March 1999)
- Justification of the algorithm for finding a spanning family for the intersection of two subspaces (html file)
- A highbrow proof of the Cayley-Hamilton theorem (html file)
- Generalised Eigenspaces (pdf file)
- A Jordan canonical form algorithm (html file)
- The LDU decomposition (html file)
- Quotient spaces (pdf file)

### Problem Sheets/Solutions

- Problem Sheet 1 (pdf file)
- Solutions, Sheet 1 (pdf file)
- Problem Sheet 2 (pdf file)
- Assignment 1 (pdf file)
- Problem Sheet 3 (pdf file)
- Problem Sheet 4 (pdf file)
- Solutions (Assignment 1)
- Assignment 2 (pdf file)
- Problem Sheet 5 (pdf file)
- Revision Problem Sheet 1 (pdf file)
- Solutions (Assignment 2)
- Problem Sheet 6 (pdf file)
- Assignment 3 (pdf file)
- Problem Sheet 7 (pdf file)
- Problem Sheet 8 (pdf file)
- Assignment 4 (pdf file)
- Solutions (Sheet 2-9)
- Solutions (Assignment 3)
- Problem Sheet 9 (pdf file)
- Solutions (Assignment 4)

### Lecture Notes

On 17/3/99 the online notes underwent a reorganisation. Lectures -1 and 0 were partly revision of first year topics. Lecture 1 then started with vector spaces. Proofs that were omitted in lectures are, in the main, presented in the online notes. They are for the interested student.- Solving systems of linear equations (pdf file) (
**Lecture -1**) - Flow-chart for the Gauss-Jordan algorithm (pdf)
- Non-singular matrices (pdf file) (
**Lecture 0**) - Transpose of a matrix (pdf file)
**Lectures 1-25**(Lecture 25 is the last one)

KRM 17th February 2003