Ing Ind - Inf (Mag.)(ord. 270) - CO (482) COMPUTER SCIENCE AND ENGINEERING - INGEGNERIA INFORMATICA

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088975 - ADVANCED LINEAR ALGEBRA

Obiettivi dell'insegnamento

The aim of this course is to provide the basic mathematical tools necessary for a Master Degree in Engineering, with a particular emphasis to Linear Algebra. The course covers the mathematical background of the most common techniques for treating linear engineering models from least squares to Gauss-Newton method and SVD. Each topic is treated not only theoretically but also practically through lab sessions that allow students to acquire a good level of autonomy in problem solving.

Risultati di apprendimento attesi

Dublin Descriptors

Expected learning outcomes

Knowledge and understanding

Understand the geometry of euclidean spaces and the associated constructions: orthogonal decomposition, Gram-Schmidt procedure, QR-decomposition

Understand the most important ideas of linear algebra from the notion of space to diagonalization and other matrix decompositions and constructions.

Recognize the linearity of many engineering problems and exploit it by applying to them the ideas of linear algebra

Understand matrix norm, minimal gain, singular values, condition number and their significance in handling errors in measures and designs

Applying knowledge and understanding

Know how to compute explicitly the most common matrix decompositions: QR, SVD, diagonalization

Extract the matrices of a linear model from input and output data

Determine when least squares is applicable and find least squares solutions

Handle multiobjective least squares problems

Find least norm solutions for underdetermined systems

Know how to apply Gauss-Newton method to nonlinear models

Know how to compute matrix norm, minimal gain, and the exponential of a diagonalizable matrix

Apply SVD to solve problems with constraints

Apply matrix exponential and diagonalization in the qualitative study of a linear autonomous systems

Argomenti trattati

The following topics are covered:

Review of basic linear algebra: vector spaces, subspaces. linear combination, linear independence, basis.

More linear algebra: scalar product, orthogonality, orthonormal basis, Gram-Schmidt orthonormalization, QR factorization.

Least-squares procedure and applications.

Regularized least-squares and Gauss-Newton method

Least-norm solutions of underdetermined equations

Eigenvectors and diagonalization

Symmetric matrices, quadratic forms, matrix norm

Singular Value Decomposition

Matrix exponential and autonomous systems

Jordan canonical form and Cayley-Hamilton theorem

Labs will be offered with detailed solutions of engineering problems using the material of the course and matlab.

Prerequisiti

The required background is limited to standard introductory courses in Calculus and Linear Algebra.

Modalità di valutazione

On course evaluation: There are a midterm and a final exam. Also lab reports will be evaluated. The midterm exam weights 30% of the final mark. The final exam weights 50% of the final mark. The lab reports weight 20% of the final mark. There will be two labs. Attendance to the labs is mandatory for acquiring the lab score.

The midterm consists of a homework on the first part of the course.

The final exam is a written examination on the syllabus of the second part of the course.

The final exam can be taken in any exam session and its score can be rejected retaining the lab and midterm scores.

Off course evaluation: a written examination on the whole syllabus including the material discussed in lectures, recitations, and labs.

Type of assessment

Description

Dublin descriptor

Written test

Solution of numerical problems

Theoretical questions

Solution of engineering models developped in class

1,2

1

1,2

Assessment of laboratorial artefacts

Solution of engineering models assigned as homework (individual) or as matlab assignment (in groups)

2

Bibliografia

S. Boys's noteshttp://www.stanford.edu/class/ee263G. Strang, Introduction to Linear Algebra, Editore: Wellesley Cambridge Press
B. Jacob, Linear Algebra

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

26:00

39:00

Esercitazione

16:00

24:00

Laboratorio Informatico

8:00

12:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

50:00

75:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

Disponibilità di materiale didattico/slides in lingua inglese

Disponibilità di libri di testo/bibliografia in lingua inglese

Possibilità di sostenere l'esame in lingua inglese

Disponibilità di supporto didattico in lingua inglese