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## Course Overview

Linear algebra is the study of vector spaces and linear maps between them and it is a central subject within mathematics.

It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.

The two courses Linear Algebra I and II aim at providing a solid foundation of the subject.

### Course Details

Study Type Level Undergraduate 2 Second Term 15 credits (7.5 ECTS credits) Aberdeen No Dr Matthew Burfitt

### Qualification Prerequisites

• Programme Level 2

None.

None.

No

### Course Description

This is the second part of the two parts course on linear algebra. The whole course contains the following topics:

* Fields
* Vector spaces
* Linear maps
* Matrices
* Linear equations
* Eigenvalues and eigenvectors

Syllabus

• The ring of polynomials with coefficients in a field.
• The various definitions of the determinant. Properties and methods of calculation. Finding the inverse of a matrix using cofactors.
• Eigenvalues and eigenvectors of square matrices and of endomorphisms. Properties.
• Diagonalization
• Minimal polynomial, characteristic polynomial, Cayley-Hamilton theorem.
• Orthogonal bases and the Gram-Schmidt procedure.
• Product spaces, symmetric matrices, orthogonal transformations, unitary transformations.
• Jordan normal forms if time allows.

### Contact Teaching Time

Information on contact teaching time is available from the course guide.

### Teaching Breakdown

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

### Summative Assessments

1st Attempt

10x Weekly online quizzes - 1% each

3x Standard assignments - 30% each

Alternative Resit Arrangements

Resubmission of failed elements (pass marks carried forward)

### Formative Assessment

There are no assessments for this course.

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberNot Available

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