Linear algebra and numerical methods

Preface

These notes were first written for the new first semester course MAT1105 - Linear algebra and numerical methods, at the University of Oslo. The course was held the first time the fall of 2024, and gives an introduction to basic mathematical thinking, linear algebra, and numerical methods. In the first version of the course, linear algebra was covered by chapter 1 and 4 in the book “Flervariabel analyse med lineær algebra” by Tom Lindstrøm (in norwegian), while the two other parts of the curriculum were covered by notes on their own. In 2025 new notes for the linear algebra part were added, and merged with the notes on numerical analysis, even though the numerical analysis builds only loosely on linear algebra.

The notes contain many proofs, but many proofs in linear algebra are quite short, and are thus suitable following the mentioned introduction to basic mathematical thinking.

The notes contain several Python programming examples, as well as an introduction to basic Python commands for linear algebra. Most students at the University of Oslo take the course IN1900 - Introduction to Programming with Scientific Applications, in parallel with the notes here. Linear algebra is a suitable testbed for Python programming, and the material contains many code snippets inspired by linear algebra. There are few figures in these notes - the role of figures is partially replaced by short programming examples with their graphical results shown. It is recommended to spend some time on the programming examples. The following commands load the python packages you need.

import numpy as np
import matplotlib.pyplot as plt
from scipy.linalg import hilbert
import sympy as sym
import math, wave, sys, os, subprocess
import pandas as pd

The notes have been typeset with the Quarto publishing system (), and come in a pdf version, and an html version. Each of these come in versions with and without solutions to the exercises.
The html versions have some features not found in the pdf versions:

Each chapter has a quiz consisting of about 10 problems, and the quizzes aggregate the number of correct answers. Interactive programming examples and exercises which use pyodide - i.e., python is embedded in the browser, without the need for a server. For this interactive programming to work well you should avoid the Safari web browser.

Parts of this material were originally based on material written by Knut Mørken for the course MAT-INF1100, Modelling and Computations, at the University of Oslo.

These notes are maintained in english. For those of you who prefer norwegian, AI will be used to create a translation.