The knowledge of the material covered in the course Linear Algebra for Computer Scientists 1 is assumed.
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.
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.
You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudymap will automatically be displayed in MyTimetable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.
MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).
For more information, watch the video or go the the 'help-page' in MyTimetable. Pleas note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.
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.
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 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.
From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudymap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information. An exemption is the fall semester for 1st year bachelor students, the student administration will enroll this group.
Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ on MyStudymap can be found here.