Cristiano Bocci
University of Siena - Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche
Course Type
Type A
Calendar
June 17-18-24 h. 15:00-18:00 aula 103 June 19-25-26 h. 15:00-18:00 aula 15
Room
Program
Abstract
The course has two main aspects: a theoretical and a practical part. In the theoretical part, main definitions, properties and results of tensors will be introduced.
In the practical part, the emphasis will be on applications of tensors in different fields.
Syllabus:
1) Tensors, decomposable tensors, rank of a tensor and related results
2) Symmetric tensors, rank for symmetric tensors, relationship between symmetric tensors and polynomials
3) Operations on tensors and related results
4) Elements of projective geometry, link between tensors and secant varieties of Segre and Veronese varieties
5) SVD and image compression
6) Typical and maximal ranks, border rank, decomposition methods
7) Applications of tensors to Applied Sciences
