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MA22020: Advanced linear algebra

[Page last updated: 09 August 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 5 [equivalent to 10 CATS credits]
Notional Study Hours: 100
Level: Intermediate (FHEQ level 5)
Period:
Semester 1
Assessment Summary: EXCB 100%
Assessment Detail:
  • Examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA12004 OR take MA12011 OR take MA12013
Learning Outcomes: By the end of this unit, you will be able to:
  • Demonstrate understanding of vector spaces and abstract linear algebra, including quotient spaces, dual spaces and bilinear forms.
  • Classify linear operators in theory and practice.
  • Compute the Jordan Normal Form of matrices.



Synopsis: This unit builds on your grounding in basic linear algebra from Year 1 to develop the general theory of abstract vector spaces. You will develop your ability to think abstractly, and to work with mathematical objects in a more abstract setting. You will learn about mathematical structure and properties, obtain major theorems, and explore the wide applicability of this theory.

Content: Vector subspaces, sums and intersections, complementary subspaces, quotients. Linear operators: review of eigenvalues and eigenvectors; eigenspaces, invariant subspaces. Minimal polynomials, Cayley-Hamilton theorem. Generalised eigenspaces, Jordan normal form theorem and applications. Further topics to be chosen from: Dual spaces and bases, transpose of a linear map, annihilators. Bilinear maps and forms. Symmetric bilinear forms: radical and rank. Quadratic forms: polarisation, diagonalisation, rank and signature.

Course availability:

MA22020 is Compulsory on the following courses:

Department of Computer Science
  • USCM-AFM32 : MComp(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AKM32 : MComp(Hons) Computer Science and Mathematics with professional placement (Year 2)
  • USCM-AKM32 : MComp(Hons) Computer Science and Mathematics with study abroad (Year 2)
Department of Physics
  • USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 2)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with professional placement (Year 2)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with study abroad (Year 2)
  • USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 2)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with professional placement (Year 2)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with study abroad (Year 2)

MA22020 is Optional on the following courses:

Department of Computer Science
  • USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 2)
  • USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with professional placement (Year 2)
  • USCM-AKB32 : BSc(Hons) Computer Science and Mathematics with study abroad (Year 2)
Department of Economics
  • UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 2)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement (Year 2)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with professional placement and study abroad (Year 2)
  • UHES-AKB12 : BSc(Hons) Economics and Mathematics with study abroad (Year 2)
Department of Mathematical Sciences
  • USMA-AFB30 : BSc(Hons) Mathematics (Year 2)
  • USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 2)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with professional placement (Year 2)
  • USMA-AKB32 : BSc(Hons) Mathematics and Statistics with study abroad (Year 2)
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 2)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 2)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 2)
  • USMA-AKB30 : BSc(Hons) Mathematics with professional placement (Year 2)
  • USMA-AKB30 : BSc(Hons) Mathematics with study abroad (Year 2)
  • USMA-AFM30 : MMath(Hons) Mathematics (Year 2)
  • USMA-AKM30 : MMath(Hons) Mathematics with professional placement (Year 2)
  • USMA-AKM31 : MMath(Hons) Mathematics with study abroad (Year 2)

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.