# Linear Algebra Review

This course will review the fundamental concepts of Linear Algebra; an essential ingredient of imaging science. Linear Algebra is usually taught during the first year of the undergraduate science and engineering program when the student is, in many cases, not yet able to appreciate its beauty and practical utility. Some of the crucial ideas/theories might not yet be fully grasped and could certainly be forgotten by the time the student becomes active as a researcher.

The aim of this course is to refresh and to deepen the student's understanding of Linear Algebra. In particular, the course will cover: systems of linear equations, linear transformations, determinants, vector spaces, linear dependency, orthogonality, orthogonal projections, least-squares problems, eigenvectors/eigenvalues, quadratic forms, singular value decomposition, rank, numerical and computational issues.

Examples and exercises will show how the theory can be applied to practical situations. Applications include: image processing, principal component analysis, optimization, dynamical systems, differential equations and Fourier Theory. **Practical information**

Instructor: Alessandro Sbrizzi (a.sbrizzi at umcutrecht.nl)

Schedule: one lesson per week on Wednesdays at 9.30. First lesson: 23 September 2015. Final lesson: 18 November 2015.

Location: Room Q0S 4.313 (also known as “sportzaal”)

Textbook: Linear Algebra and its Applications, David Lay, Addison-Wesley (preferably the 4th edition) **How to enroll**

Everybody is welcome to participate but only a limited number of places are available. Please enroll by sending me an email: a.sbrizzi at umcutrecht.nl.