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degree courses
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School of Science
Course unit
LINEAR ALGEBRA (Ult. numero di matricola dispari)
SCP4063450, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course First cycle degree in
SC2095, Degree course structure A.Y. 2014/15, A.Y. 2018/19
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination LINEAR ALGEBRA
Website of the academic structure
Department of reference Department of Statistical Sciences
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ALBERTO TONOLO MAT/02

Course unit code Course unit name Teacher in charge Degree course code
SCP4063450 LINEAR ALGEBRA (Ult. numero di matricola dispari) ALBERTO TONOLO SC2094

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/02 Algebra 6.0

Course unit organization
Period First semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 22 28.0 No turn
Lecture 4.0 32 68.0 No turn

Start of activities 01/10/2018
End of activities 18/01/2019
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
12 Commissione a.a.2019/20 (matr.pari) 01/10/2019 30/09/2020 PARMEGGIANI GEMMA (Presidente)
CESARONI ANNALISA (Membro Effettivo)
TONOLO ALBERTO (Membro Effettivo)
11 Commissione a.a.2019/20 (matr.dispari) 01/10/2019 30/09/2020 TONOLO ALBERTO (Presidente)
CESARONI ANNALISA (Membro Effettivo)
PARMEGGIANI GEMMA (Membro Effettivo)
10 Commissione a.a.2018/19 (matr. pari) 01/10/2018 30/09/2019 PARMEGGIANI GEMMA (Presidente)
CESARONI ANNALISA (Membro Effettivo)
MANNUCCI PAOLA (Membro Effettivo)
TONOLO ALBERTO (Membro Effettivo)
9 Commissione a.a.2018/19 (matr.dispari) 01/10/2018 30/09/2019 TONOLO ALBERTO (Presidente)
CESARONI ANNALISA (Membro Effettivo)
MANNUCCI PAOLA (Membro Effettivo)
PARMEGGIANI GEMMA (Membro Effettivo)

Prerequisites: Elementary algebra, trigonometry, elementary analytical geometry.
Target skills and knowledge: The aim of the course is to introduce students to the following topics in Linear Algebra: systems of linear equations, their theoretical and algorithmic solutions, basic concepts of the theory of real and complex Euclidean vector spaces, calculation of the determinant of a matrix, basic results on the eigensystems, up to the Spectral Theorem.
Examination methods: Only written exam. 
Four exercises have to be solved within three hours. 
The consultation of books or notes is not allowed. 
The presence for the registration of the exam is mandatory.
Assessment criteria: Each question of each exercise contributes for a certain specified amount to the maximum mark of 33/30 (corresponding to 30 cum laude). 
The criteria for a positive evaluation are correctness, precision and completeness of the solutions of the different exercise.
Course unit contents: Matrices and their operations. The transpose of a matrix. Block decomposition of matrices. Gauss elimination for the algorithmic resolution of systems of linear equations and the calculation of inverse matrices. Elementary matrices and LU decomposition. 

Vector spaces. Spanning sets. Linear dependence and independence. Basis and dimension. The four fundamental subspaces of a matrix. Coordinates of a vector with respect to an ordered basis. Change of bases. Linear transformations and associated matrices. 

Norms and inner products. Orthogonal vectors and orthonormal bases. Orthogonal projections. Gram-Schmidt procedure. QR decomposition. Least squares approximation and normal equations. 

Calculation of the determinant of a matrix and applications. 

Eigenvalues, eigenvectors and eigenspaces. Characteristic polynomial and its properties. Algebraic and geometric multiplicities of eigenvalues. Diagonalization and triangularization of matrices. Normal matrices and the Spectral Theorem.
Planned learning activities and teaching methods: 54 hours of class, a third of which is dedicated to numerical exercises. Also homework problems are given.
Additional notes about suggested reading: The course program is completely covered by the first three chapters and some paragraphs of chapters 4, 5 and 6 of the textbook: "Algebra Lineare", E. Gregorio, L. Salce, ed. Libreria Progetto, Padova 2012 (3^ ed.). In addition, 
appendices A, B and C of this textbook are used. 
Homework problems and other material can be found on the webpage:
Textbooks (and optional supplementary readings)
  • E. GREGORIO, L. SALCE, Algebra Lineare. Padova: Libreria progetto, 2012. terza edizione Cerca nel catalogo
  • NOBLE B., DANIEL J.W., Applied Linear Algebra. Englewood Cliffs. NJ, USA: Prentice-Hall Inc., 1988. Cerca nel catalogo

Innovative teaching methods: Teaching and learning strategies
  • Problem solving
  • Loading of files and pages (web pages, Moodle, ...)

Innovative teaching methods: Software or applications used
  • Moodle (files, quizzes, workshops, ...)