## Admission Requirements

Lineaire Algebra 1 or 1NA

## Description

This course is a direct continuation of the course Linear Algebra 1NA. On the one hand a couple of new subjects are treated, on the other hand more emphasis is laid on a more abstract treatment and vector spaces over complex numbers are considered. It is in this more abstract form that the power of the subject becomes manifest. Abstract linear algebra lies at the basis of modern Quantum Mechanics. Attention is given to a few applications in physics, mainly in the filed of Classical Mechanics.

## Course Objectives

After finishing this course you have an operational knowledge of the following concepts and you are able to make (simple) problems concerning the following subjects:

real and complex vector spaces

linear maps, the matrix of a linear maps

scalar products on vector spaces

orthogonality, orthogonal projections

transformations of bases

special linear maps: hermitian, unitary, orthogonal, normal maps

quadratic and hermitian forms

spectral theorems

## Timetable

Schedule

For detailed information go to Timetable in Brightspace

## Mode of instruction

See Brightspace

## Assessments

written exam with open questions

(optional) homework

By handing in homework (optional!) a bonus of 0.5 maximum can be earned that will be added to the grade of the exam. This bonus is only given if the total grade of the exam is at least 5.5.

In the same academic year a retake exam will be organised. This will be in the form of a single exam about the entire course matter. The homework bonus grade is not valid for the retake.

## Brightspace

Instructions and course material can be found on Brightspace. Registration for Brightspace occurs automatically when students enroll in uSis via uSis by registration for a class activity using a class number

## Reading list

Lecture notes can be downloaded via Brightspace. It is also possible to purchase a hard copy at the secretariat of the Mathematical Institue (Snellius building).

## Contact

Dr. Robert-Jan Kooman kooman@math.leidenuniv.nl Contactgegevens docent: Dr. R.J. Kooman

## Remarks

Students who are doing a double bachelor Natuurkunde met Wiskunde of Sterrenkunde met Wiskunde, take the course Lineaire algebra 2 with Mathematics.