
Course unit
LINEAR ALGEBRA (Ult. numero di matricola pari)
SCP4063450, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary 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 
Hours of Individual study 
Shifts 
Practice 
2.0 
22 
28.0 
No turn 
Lecture 
4.0 
32 
68.0 
No turn 
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 exercises are designed to assess the student's ability to work with the mathematical concepts introduced in class.
The consultation of books or notes is not allowed.
The presence for the registration of the exam is mandatory. 
Assessment criteria:

The criteria for a positive evaluation are:
 correctness and completeness of the solutions of the exercises
 proper use of mathematical language 
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. GramSchmidt 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: http://www.math.unipd.it/~parmeggi/mat_gemma.html 
Textbooks (and optional supplementary readings) 

E. GREGORIO, L. SALCE, Algebra Lineare. Padova: Libreria Progetto, 2012. terza edizione

NOBLE B., DANIEL J.W., Applied Linear Algebra. Englewood Cliffs, NJ, USA: PrenticeHall Inc., 1988. terza edizione

Innovative teaching methods: Teaching and learning strategies
 Problem solving
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