## Admission requirements

## Description

Linear algebra is the core language of multivariate mathematics. Matrices and matrix algebra are the quintessential framework used to organize multidimensional data and to represent basic relations, operations and transformations between these data. In particular, they enable to express concisely and with clarity many of the concepts and situations arising in statistics and data analysis.

This course will introduce basic concepts of matrix algebra and vector spaces, highlighting the geometry of linear transformations, prioritizing intuition over (manual) computation, and illustrating concrete uses of matrix algebra in statistics and other quantitative sciences.

**Topics covered:**

Systems of linear equations

Operations with matrices and vectors

Linear transformations

Rank of a matrix

Trace and determinant of a matrix

Inverse of a matrix

Symmetric, triangular, diagonal, and orthogonal matrices

Eigenvalues and eigenvectors

Diagonalization of square matrices

Vector spaces and subspaces

Linear independence and bases

Orthogonality and projections

The spectral theorem and singular value decomposition

Inner products, quadratic forms and metrics

## Course Objectives

After successful completion of this course, students are expected to be able to:

Recall definitions and explain basic concepts in linear algebra

Identify whether certain algorithms / matrix operations are applicable / theoretically feasible

Perform elementary matrix operations and perform simple computations with matrices

Verify the validity of a short matrix computation

Relate properties of matrices to properties of linear transformations

In the context of linear algebra, draw conclusions from information available and/or from the results of computations performed

In the context of statistics, express equations and relationships in the language of matrix algebra

Correctly follow and report mathematical reasoning and argumentation

## 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.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

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

Lectures and workgroups.

## Assessment method

The assessment is fully based on a written exam. The exam consists of open-ended and/or short-answer and/or multiple-choice questions. Multiple-choice and short-answer questions will assess the knowledge and understanding of the topics covered. Open-ended questions will be mathematical exercises similar to those assigned during the tutorials. Such questions are graded based on accuracy of the answer, correct implementation of the method used, and critical reflection on the results found.

## Reading list

Required materials:

W. Keith Nicholson – Linear algebra with applications. Available for free from: https://lyryx.com/linear-algebra-applications/

3Blue1Brown – The essence of linear algebra (online videos). https://www.3blue1brown.com/topics/linear-algebra

Lecture slides and exercises (with answers or solutions to some of them) will be provided via Brightspace.

Additional materials:

John Fox – Appendix B to Applied regression analysis and generalized linear models

David A. Harville – Matrix algebra form a statistician’s perspective

Shayle R. Searle and André I. Khuri – Matrix algebra useful for statistics

## 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

See this page for more information about deadlines and enrolling for courses and exams.

**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

## 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.