MP204/MP274 Linear Algebra II/IIH

Semester 1, 1999

Course Outline

The course is designed to introduce students to linear algebra. Historically the subject arose from the study of linear equations, but now has applications to many branches of mathematics, as well as to engineering and economics.

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.


Reference books

There are many books in the PSE and Undergraduate Libraries which touch on the subject. Here are some useful ones : The books of Anton, Larson and Edwards and Leon are recommended and copies are kept at desk (KAD) in the PSE library
  1. Elementary Linear Algebra, H. Anton, QA184.A571984 (KAD)
  2. Linear Algebra and Applications, C. Cullen, QA184. C851988
  3. Linear Algebra, C.W. Curtis, QA184.C871984
  4. Linear Algebra, S.H. Friedberg, A.J. Insel, L.E. Spence, QA184.F81989
  5. Elementary Linear Algebra, R.E. Larson and B.H. Edwards, QA184.L391991 (KAD)
  6. Linear Algebra with Applications, S.J. Leon, QA184.L461 998 (KAD)
  7. Linear Algebra, S. Lipschutz, QA251.L531991
  8. Fundamental structures of algebra, G.D. Mostow, J.H. Sampson, J.-P. Meyer, QA154 .M86 1963 (honours standard)
  9. Linear Algebra, M. O'Nan, QA184.O51976
  10. Linear Algebra, L. Smith, QA184.S6319781
  11. Matrix theory and linear algebra, I.N. Herstein, David J. Winter, QA188 .H47 1988

    Various handouts

    Problem Sheets/Solutions

    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.

    KRM 17th February 2003