Several years ago, David Zmiaikou obtained his Ph.D. degree at the University Paris-Sud (Orsay) under the supervision of Professor Jean-Christophe Yoccoz. After that, he visited the mathematical institute IMPA in Rio de Janeiro thanks to the Balzan research project of Professor Jacob Palis. As a part of David's European Post-Doctoral Institute (EPDI) fellowship, he worked at:

**• **Erwin Schrodinger Institute for Mathematical Physics, Vienna, Austria

**• **Institute for Mathematical Research, Zurich, Switzerland

**• **Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France

**• **Max Planck Institute for Mathematics Bonn, Germany

Afterwards, David did postdoctoral research in DNA analysis at the Wellcome Trust Sanger Institute in the United Kingdom.

During the module, students will deepen their knowledge of linear algebra. They will learn new key concepts and methods that will help them in solving the majority of problems related to the study of linear transformations of vector spaces. Some of these concepts and methods are applied to biology, economics, computer graphics, electrical engineering and cryptography.

**SKILLS:**

- Algorithms

- Combinatorics

- Data analysis

- Discrete optimization

- Dynamical systems

- Geometry

- Group theory

- Software engineering

- Web Design

**DATE: **9 - 27 Apr, 2018

**DURATION: **3** **Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

**LOCATION: **__Barcelona, Harbour.Space Campus__

**COURSE TYPE: **Offline

WHAT YOUWILL LEARN

COURSE OUTLINE

ABOUT DAVID

BIBLIOGRAPHY

**HARBOUR.SPACE **

In this module, the beautiful and powerful results of linear algebra will be explored. One of the most important tools in the study of matrices is Jordan canonical form which allows to simplify many calculations (e.g. exponentiation).

We will learn how to find such a canonical form and apply that knowledge to special classes of matrices. Furthermore, bilinear forms will be introduced together with the classical notion of a Euclidean space. An algorithm called Gram–Schmidt Process will provide a useful technique for constructing orthonormal bases of a Euclidean space and its subspaces.

DAVIDZMIAIKOU

HARBOUR.SPACEUNIVERSITY

**DATE: **9 – 27 Apr, 2018

**DURATION: **3 Weeks

**LECTURES: **3 Hours per day

**LANGUAGE: **English

**LOCATION: **__B____arcelona, Harbour.Space Campus__

**COURSE TYPE: **Offline

**Session 2**

Minimal Polynomial of a Matrix

**Session 3**

Special Matrices

**Session 1**

Algebraic Prerequisites

All rights reserved. 2018

**Session 4**

Duality

We will learn how to find such a canonical form and apply that knowledge to special classes of matrices. Furthermore, bilinear forms will be introduced together with the classical notion of a Euclidean space. An algorithm called Gram–Schmidt Process will provide a useful technique for constructing orthonormal bases of a Euclidean space and its subspaces.

In this module, the beautiful and powerful results of linear algebra will be explored. One of the most important tools in the study of matrices is Jordan canonical form which allows

to simplify many calculations (e.g. exponentiation).

We will learn how to find such a canonical form and apply that knowledge to special classes of matrices. Furthermore, bilinear forms will be introduced together with the classical notion of a Euclidean space. An algorithm called Gram–Schmidt Process will provide a useful technique for constructing orthonormal bases of a Euclidean space and its subspaces.

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