## 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

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. Please 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

## 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

It is the responsibility of every student 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.

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's on MyStudymap can be found here.