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
  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
  6. Linear Algebra with applications, Steven Leon, QA184 .L46 1998
  7. Linear Algebra, S. Lipschutz, QA251.L531991
  8. Linear Algebra, M. O'Nan, QA184.O51976
  9. Linear Algebra, L. Smith, QA184.S6319781
  10. 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

    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