# MATH202 Linear Algebra

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.

Paper title Linear Algebra MATH202 Mathematics 0.1500 18 points Second Semester \$904.05 \$3,954.75
Prerequisite
MATH 170
Restriction
MATH 242, MATH 341
Schedule C
Arts and Music, Science
Eligibility
MATH 202 is compulsory for the Mathematics major and is of particular relevance, also, for students majoring in Statistics, Computer Science and Physics.
Contact

Dr Dominic Searles, ext 7762, dsearles@maths.otago.ac.nz

Teaching staff

Dr Dominic Searles

Paper Structure

Main topics:

• 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
Textbooks

Sheldon Axler, Linear Algebra Done Right, 3rd ed, Springer (free to download e-book through UoO library)

Course outline
View course outline for MATH 202
Critical thinking.
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.

## Timetable

### Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
L1 Monday 09:00-09:50 28-34, 36-41
Wednesday 09:00-09:50 28-34, 36-41
Friday 09:00-09:50 28-34, 36-41

#### Tutorial

Stream Days Times Weeks
Attend one stream from
T1 Monday 14:00-14:50 29-34, 36-41
T2 Tuesday 11:00-11:50 29-34, 36-41
T3 Wednesday 14:00-14:50 29-34, 36-41

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, and the spectral theorem.

We will explore applications of these ideas in science, computer science and engineering.

Paper title Linear Algebra MATH202 Mathematics 0.15 18 points Second Semester Tuition Fees for 2021 have not yet been set Tuition Fees for international students are elsewhere on this website.
Prerequisite
MATH 170
Restriction
MATH 242, MATH 341
Schedule C
Arts and Music, Science
Eligibility

MATH 202 is compulsory for the Mathematics major. It is particularly important for students majoring in Statistics, Computer Science and Physics, and is relevant and useful for any student in the sciences who forsees themselves working with and analysing data.

Contact

Dr Dominic Searles, ext 7762, dsearles@maths.otago.ac.nz

Teaching staff

Dr Dominic Searles

Paper Structure

Main topics:

• Vector spaces over the real and complex numbers (mainly finite-dimensional), vector subspaces
• Linear combinations, linear independence and span, bases, dimension, extending bases of subspaces, sum of subspaces, direct sums
• Linear transformations and their properties, kernel and range, rank-nullity theorem
• Representation of linear transformations by matrices, coordinate vectors, composition of linear transformations corresponds to products of matrices
• Diagonalisation, invariant subspaces, eigenvalues and eigenvectors
• Inner products, orthogonality, orthogonal projections, Cauchy-Schwartz inequality, inner-product norm, orthonormal bases, Gram-Schmidt process, orthogonal complements, minimisation problems
• The adjoint of a linear transformation, self-adjoint and normal transformations, the real and complex spectral theorems, the singular-value decomposition of a matrix
Textbooks

Sheldon Axler, Linear Algebra Done Right, 3rd ed, Springer (free to download e-book through UoO library)

Course outline
View course outline for MATH 202
Critical thinking.
Learning Outcomes

Students who successfully complete this paper will develop a working knowledge of the central ideas of linear algebra and the applications of these ideas in science, computer science and engineering.

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

## Timetable

### Second Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
A1 Monday 09:00-09:50 28-34, 36-41
Wednesday 09:00-09:50 28-34, 36-41
Friday 09:00-09:50 28-34, 36-41

#### Tutorial

Stream Days Times Weeks
Attend one stream from
A1 Monday 14:00-14:50 29-34, 36-41
A2 Tuesday 11:00-11:50 29-34, 36-41
A3 Wednesday 14:00-14:50 29-34, 36-41