Red X iconGreen tick iconYellow tick icon


    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.

    About this paper

    Paper title Linear Algebra
    Subject Mathematics
    EFTS 0.15
    Points 18 points
    Teaching period Semester 1 (On campus)
    Domestic Tuition Fees ( NZD ) $981.75
    International Tuition Fees Tuition Fees for international students are elsewhere on this website.
    MATH 140 or MATH 170
    MATH 242, MATH 341
    Schedule C
    Arts and Music, Science

    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.


    For more information, contact MATH and COMO200-300 Level Advisor Jõrg Hennig at

    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

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

    Graduate Attributes Emphasised
    Critical thinking.
    View more information about Otago's graduate attributes.
    Learning Outcomes

    Students who successfully complete this paper will develop a working knowledge of the central ideas of linear algebra, such as:

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

    Students will also learn the applications of these ideas in science, computer science and engineering.


    Semester 1

    Teaching method
    This paper is taught On Campus
    Learning management system


    Stream Days Times Weeks
    A1 Monday 09:00-09:50 9-13, 15-22
    Wednesday 12:00-12:50 9-13, 15-22
    Friday 09:00-09:50 9-12, 15-22


    Stream Days Times Weeks
    Attend one stream from
    A1 Monday 15:00-15:50 9-13, 15-22
    A2 Tuesday 11:00-11:50 9-13, 15-22
    A3 Wednesday 13:00-13:50 9-13, 15-22
    Back to top