# Linear Algebra for Computer Scientists 2

Course
2024-2025

The knowledge of the material covered in the course Linear Algebra for Computer Scientists 1 is assumed.

## Description

In this course we introduce the concept of vector spaces and their dimension. We study further properties of matrices such as their null space, their column space, rank, eigenvalues, and eigenvectors, leading to matrix diagonalisation. Furthermore, the concepts of orthogonality, including the Gramm-Schmidt algorithm, and the distance between vectors are discussed covered. We also study applications such as the least square method for linear approximation.

## Course objectives

Upon successful completion of the course, a student will be able to:

• Explained the concept of a vector space and a vector subspace, and give examples of vector spaces.

• Identify vector subspaces associated to a matrix.

• Compute eigenvalues and eigenvectors of a matrix, and diagonalize a matrix if possible.

• Explain the concept of inner product and distance in vector spaces, and be able to compute those.

• Determine if given vectors are orthogonal, and construct an orthogonal basis of a vector space using the Gramm-Schmidt algorithm.

• Explain the method of the least squares linear approximation.

## Timetable

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

There will be a weekly lecture and a weekly problem session (tutorial). Homework will be assigned after each lecture. During the problem sessions, the students will have the opportunity to ask questions about the material covered so far and check their homework solutions. Homework will not be collected, but used as a tool to prepare for weekly quizzes. Quizzes will take place during the tutorial (except the first week), will be 15-20 minutes long. Quizzes will be graded, and the grade for quizzes contribute a bonus point to the final grade.

## Assessment method

Written exam, in-class written quizzes administered during tutorials.

Students can earn a bonus of maximum 1 point on their exam grade by participating in in-class quizzes. There will be a total of six quizzes, one lowest grade for the quizzes will be dropped. The remaining five grades for quizzes will make equal parts of the bonus. The quizzes are not required for passing the course and do not have a resit opportunity.

The final grade is determined by adding bonus to the grade of the written exam, and then rounding off to the nearest half integer (e.g. 7.24 becomes 7 and 7.25 becomes 7.5). The final grade can never be more than a 10.

David. C. Lay: *Linear Algebra and its Applications, Addison-Wesley. *
This book will be required for the course; weekly problem sessions will be based on it, and essential reading will be set from it. The 5th international edition is recommended, but other editions are also OK, just be aware that the page numbers for the required reading may be incorrect.

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Education coordinator LIACS bachelors

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.