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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 Sub Session 15 credits (7.5 ECTS credits) Aberdeen No Dr Fabian Hebestreit

### Qualification Prerequisites

• Programme Level 2

None.

None.

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### 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

• 3 Lectures during University week s 26 - 35, 39
• 1 Tutorial during University week s 27 - 35, 39

### Summative Assessments

#### Homework

Assessment Type Weighting Summative 20 In-course assignments will normally be marked within one week and feedback provided to students in tutorials.
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Class Test

Assessment Type Weighting Summative 10 10 x Weekly Quizzes
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Exam

Assessment Type Weighting Summative 50 Students will be invited to contact Course Coordinator for feedback on the final examination.
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

#### Homework

Assessment Type Weighting Summative 20 In-course assignments will normally be marked within one week and feedback provided to students in tutorials.
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Formative Assessment

There are no assessments for this course.

### Resit Assessments

#### Exam

Assessment Type Summative Best of (resit exam mark) or (resit exam mark combined with CA marks).
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberNot Available

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