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 |
---|---|

Paper code | MATH202 |

Subject | Mathematics |

EFTS | 0.1500 |

Points | 18 points |

Teaching period | Second Semester |

Domestic Tuition Fees (NZD) | $904.05 |

International Tuition Fees (NZD) | $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

- More information link
- View more information about MATH 202
- Teaching staff
- 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
- Graduate Attributes Emphasised
- Critical thinking.

View more information about Otago's graduate attributes. - 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

## Timetable

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 |
---|---|

Paper code | MATH202 |

Subject | Mathematics |

EFTS | 0.15 |

Points | 18 points |

Teaching period | Second Semester |

Domestic Tuition Fees | Tuition Fees for 2021 have not yet been set |

International Tuition Fees | 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

- More information link
- View more information about MATH 202
- Teaching staff
- 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
- 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 and the applications of these ideas in science, computer science and engineering.

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