Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Module Offerings
4110MATHS-SEP-CTY
Aims
To provide an introduction to Linear Algebra with a view towards solving real-world problems. Complete a Future Focus e-learning task.
Learning Outcomes
1.
Use the fundamental notions of linear independence, dimension, linearity of a map and orthogonality in concrete examples and real-world applications.
2.
Solve systems of linear equations. Derive the conditions for existence and uniqueness of solutions from the vector space structure defined by a system of linear equations.
3.
Characterise properties of matrices/linear maps (e.g., eigenvalues and eigenvectors; orthogonality) and exploit the results of this analysis in real-world applications.
4.
Identify and reflect upon the following aspects of self-awareness in respect of personal development and career planning: strength and weaknesses, motivations and values, ability to work with others.
Module Content
Outline Syllabus:Systems of linear equations: Gaussian elimination and the solution space of linear systems.
Vector spaces, Sub-vector spaces and their geometry, Spanning sets.
Basis and Dimension of a vector space.
Linear maps and matrices. Kernel and image.
Invertible matrices and determinants.
Eigenvectors and eigenvalues. Characteristic polynomial. Matrix diagonalisation.
Scalar products and orthogonality. Orthogonality and linear independence.
Module Overview:
This module provides you with the experience of using pencil-and-paper techniques and mathematical software to solve realistic problems in Linear Algebra.
This module provides you with the experience of using pencil-and-paper techniques and mathematical software to solve realistic problems in Linear Algebra.
Additional Information:This module provides students with the experience of using pencil-and-paper techniques and mathematical software to solve realistic problems in Linear Algebra.