Linear Algebra - MAT00008I

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  • Department: Mathematics
  • Module co-ordinator: Dr. David Ferguson
  • Credit value: 20 credits
  • Credit level: I
  • Academic year of delivery: 2019-20
    • See module specification for other years: 2016-17

Module will run

Occurrence Teaching cycle
A Spring Term 2019-20 to Summer Term 2019-20

Module aims

  • To develop the theory of vector spaces by extending the ideas presented in Core Algebra.
  • To characterise matrices in terms of their Jordan normal form, and hence prescribe when they can be diagonalised and when they cannot.
  • To describe the main properties of normal matrices (eg. symmetric, hermitian, orthogonal, unitary).
  • To find some decompositions of matrices.
  • To develop the theory of quadratic forms.

Module learning outcomes

At the end of the module you should:

  • Be comfortable with the axiomatic definition of a vector space.
  • Deduce simple properties of vector spaces from the axioms.
  • Represent linear maps by matrices.
  • Understand the concepts of inner product and inner product space.
  • Understand the main properties of hermitian, unitary and normal matrices and linear maps.
  • Understand why the Cayley-Hamilton Theorem is true, and find the algebraic, minimal and geometric multiplicities of eigenvalues of a square matrix.
  • Understand the Jordan normal form of a square matrix.
  • Decide whether a given matrix can be diagonalised.
  • Understand some bilinear, quadratic and hermitian forms and be able to diagonalise them.

Assessment

Task Length % of module mark
University - closed examination
Closed Examination
3 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
University - closed examination
Closed Examination
3 hours 100

Module feedback

Information currently unavailable

Indicative reading

R B J T Allenby, Linear Algebra, Arnold (S 2.897 ALL).

R Kaye and R Wilson, Linear Algebra, OUP (S 2.897 KAY).

D C Lay, Linear Algebra and its applications, Addison Wesley (S 2.897 LAY).

J. B. Fraleigh and R. A. Beauregard, Linear Algebra, Addison Wesley (S 2.897 FRA).

P. R. Halmos, Linear Algebra Problem Book, MAA ( S 2.897 HAL)



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.