Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
Repeat examination Array 

Description This module is a second course in linear algebra. In this module students will consider abstract vector spaces and linear transformations and will study the various canonical forms for matrices. The participants are expected to have a proficiency with geometric vectors and matrices. This module provides the linear algebra tools for for such courses as vector calculus and probability. Students are expected to attend lectures, participate in tutorials and take inclass tests.  
Learning Outcomes 1. Give selected definitions and prove selected theorems 2. Demonstrate an understanding of the mechanics of change of basis. 3. Compute canonical forms for matrices. 4. Apply the spectral theorem for real symmetric matrices.  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and Learning Activities
Vector spaces Abstract vector spaces and linear transformations. Ranknullity theorem Matrix representations Coordinates, matrix representations, similarity. Projection Inner products, orthogonal vectors, projection, least squares. Complex matrices. Complex vector spaces and matrices, complex inner product, unitary similarity, spectral theorem. Jordan canonical form HamiltonCayley theorem, primary decomposition, Jordan bases, Jordan forms.  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes  
Date of Last Revision  28JAN10  
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