### Module Details

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title Linear Algebra and Geometry Code MATH244 Coordinator Dr A Pratoussevitch Mathematical Sciences Anna.Pratoussevitch@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2021-22 Level 5 FHEQ First Semester 15

### Aims

To introduce general concepts of linear algebra and its applications in geometry and other areas of mathematics.

### Learning Outcomes

(LO1) To understand the geometric meaning of linear algebraic ideas.

(LO2) To know the concept of an abstract vector space and how it is used in different mathematical situations.

(LO3) To be able to apply a change of coordinates to simplify a linear map.

(LO4) To be able to work with matrix groups, in particular GL(n), O(n) and SO(n),.

(LO5) To understand bilinear forms from a geometric point of view.

(S1) Problem solving skills

(S2) Numeracy

### Syllabus

Review of linear algebra from MATH103.

Real vector spaces, bases and dimension of a vector space.

Linear maps and matrices. Change of basis.

Endomorphisms, eigenvalues, eigenvectors and eigenspaces. Geometric interpretations. Diagonalisation.

Applications to linear geometry and differential equations.

Invertible endomorphisms and the group GL(n).

Jordan Normal Form.

Bilinear forms and diagonalisation.

Orthogonal matrices and isometries. Applications to the classification of conics and quadric surfaces.

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final Assessment Standard UoL penalty applies for late submission. This is an anonymous assessment.  60 minutes    50
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
homework 1 Standard UoL penalty applies for late submission. This is not an anonymous assessment.  equivalent to 2-5 si    12
Homework 2 Standard UoL penalty applies for late submission. This is not an anonymous assessment  equivalent to 2-5 si    12
homework 3 Standard UoL penalty applies for late submission. This is not an anonymous assessment  equivalent to 2-5 si    12
Homework 4 Standard UoL penalty applies for late submission. This is not an anonymous assessment  equivalent to 2-5 si    12