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00005 - Algebra

Academic Year 2018/2019

                
                        Docente:
                        Daniele Ritelli
                    
                        Credits:
                        6
                    
                        SSD:
                        MAT/03
                    
                        Language:
                        Italian
                    
                        Teaching Mode:
                        Traditional lectures
                        
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Statistical Sciences (cod. 8873)

                            Teaching resources on Virtuale

Learning outcomes

The aim of this course is to provide a standard introduction to linear algebra and matrix analysis.
Students should:
- be familiar with basic concepts and properties of finite dimensional real vector spaces
- be familiar with algebra of real matrices
- be able to solve linear systems
- be familiar with basic concepts and properties of euclidean spaces
- have acquaintance of linear transformation between vector spaces and their representation by matrices
- be able to diagonalize a linear operator or a square matrix
- be able to classify real quadratic forms.

Course contents

Finite dimensional real vector spaces. Subspaces, linear dependence, bases and dimension.
Matrix algebra. Rank of a matrix. Determinants. Systems of linear equations.
Linear transformations and matrices. Change of basis. Diagonalization of a matrix.
Inner product spaces: norms , distances, orthogonal vectors. Orthogonal projections and least squares solutions for a linear system. Diagonalization of symmetric matrices, spectral theorem.
Real quadratic forms. Positive definite (semi)definite quadratic forms.

Readings/Bibliography

Lecture notes downloadable from the lecturer site.
L. Robbiano, Linear Algebra for everyone, Springer Verlag 2010
C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.

Teaching methods

Lessons ex cathedra. Classroom exercises, homework

Assessment methods

Written examination, where is possible to use calculators and self made formularies. The detailed explanation of all the passages is strongly requested. The aim of the exam is to detect the capability of the student to face both theoretical and practical problems in Linear Algebra.

Teaching tools

Lessons ex-cathedra using video beamer and blackboard. Homework. Computer algebra exercises.

Links to further information

https://www.dropbox.com/s/h4occ96pmiae1ws/CV_dr.pdf?dl=0

Office hours

See the website of Daniele Ritelli