# Linear Algebra

University of Otago

## Course Description

• ### Course Name

Linear Algebra

• ### Host University

University of Otago

• ### Location

Dunedin, New Zealand

• ### Area of Study

Algebra, Mathematics

• ### Language Level

Taught In English

MATH 170

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

18
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

This paper is an introduction to the fundamental ideas and techniques of linear algebra and the application of these ideas to computer science and the sciences.

The principal aim of this paper is for students to develop a working knowledge of the central ideas of linear algebra: vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, the spectral theorem and the applications of these ideas in science, computer science and engineering.

In particular, the paper introduces students to one of the major themes of modern mathematics: classification of structures and objects. Using linear algebra as a model, the paper investigates techniques that allow you to tell when two apparently different objects can be treated as if they were the same.

Course Structure
Main topics:

• One-to-one and onto functions
• Basic group theory (definition, subgroups, group homomorphisms and isomorphisms)
• Vector spaces over the real and complex numbers (mainly finite-dimensional)
• Linear transformations and their properties, kernel and range, examples involving Euclidean spaces, spaces of polynomials, spaces of continuous functions
• Linear combinations, linear independence and spans, bases, dimension, standard bases, extending bases of subspaces, coordinate vectors and isomorphisms, rank-nullity theorem
• Representation of linear transformations by matrices
• Diagonalisation, eigenvalues and eigenvectors
• Inner products, orthogonality, orthogonal projections, Cauchy-Schwartz inequality, inner-product norm, orthonormal bases, Gram-Schmidt process, orthogonal complements, minimisation problems
• the spectral theorem for matrices, singular-value decomposition of a matrix

Learning Outcomes
To develop a working knowledge of the central ideas of linear algebra:

• Vector spaces
• Linear transformations
• Orthogonality
• Eigenvalues and eigenvectors
• The spectral theorem

And the applications of these ideas in science, computer science and engineering.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.