First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Engineering
CHEMICAL AND MATERIALS ENGINEERING
Course unit
TOPICS IN LINEAR ALGEBRA AND GEOMETRY
IN08122537, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course First cycle degree in
CHEMICAL AND MATERIALS ENGINEERING
IN1840, Degree course structure A.Y. 2011/12, A.Y. 2017/18
N0
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination TOPICS IN LINEAR ALGEBRA AND GEOMETRY
Website of the academic structure http://icm.dii.unipd.it/ingegneria-chimica-e-dei-materiali/
Department of reference Department of Industrial Engineering
E-Learning website https://elearning.unipd.it/dii/course/view.php?idnumber=2017-IN1840-000ZZ-2017-IN08122537-N0
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
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

Lecturers
Teacher in charge MATTEO LONGO MAT/03

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Basic courses MAT/02 Algebra 4.0
Basic courses MAT/03 Geometry 5.0

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

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 9.0 72 153.0 No turn

Calendar
Start of activities 26/02/2018
End of activities 01/06/2018
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
5 A.A. 2018/19 01/10/2018 30/11/2019 LONGO MATTEO (Presidente)
CANDILERA MAURIZIO (Membro Effettivo)
CAILOTTO MAURIZIO (Supplente)
4 A.A. 2016/17 01/10/2016 30/11/2017 LONGO MATTEO (Presidente)
CANDILERA MAURIZIO (Membro Effettivo)

Syllabus
Prerequisites: Nothing required in advance
Target skills and knowledge: Basic notions in linear algebra and their fundamental applications to geometry, with particular attention
devoted to the study of vector spaces, linear functions and linear systems. Spectral theorem and its applications.
Assessment criteria: Written exam
Course unit contents: Introduction to linear algebra with a view to its main applications to analytic geometry.
Planned learning activities and teaching methods: Real vector spaces and subspaces. The real vector space R^n; the vector space of mxn matrices with real entries.
The vector space of polynomials in one variable with real coefficients.
Finetely generated vector spaces.
Intersection, union and sum of subspaces.
Bases and their existence. Dimension of a vector space.
Coordinates of a vector with respect to a basis.
Direct sums. Grassmann formula and its applications.
Linear functions. Definition of a linear function: existence and uniqueness conditions.
Kernel and image. Injective and surjective functions. Rank-nullity Theorem.
Preimage. Matrices associated to a linear function. Rank of a matrix.
Linear systems. Rouche'-Capelli Theorem.
Elementary row operations. Reduction to row echelon form. Systems of linear equations.
Systems of linear equations depending on a parameter.
Product of matrices, composition of linear maps. Invertible square matrices and
the computation of the inverse of an invertible matrix. Changes of bases.
Conjugated matrices.
The determinant of a matrix and its properties.
Eigenvalues and eigenvectors of an endomorphism. Eigenspaces.
Characteristic polynomial. Algebraic and geometric multiplicities.
Spectral Theorem.
Inner product. The standard inner product.
Cauchy-Schwarz inequality and triangular inequality.
Orthogonal vectors and orthogonal subspaces.
Gram-Schmidt orthogonalization.
Orthogonal projection.
Isometries, orthogonal matrices.
Symmetric matrices.
Complex numbers. Spectral Theorem for symmetric matrices.
n-dimensional affine space. Description and properties of linear manifolds.
Euclidean space. Orthogonal submanifolds.
Vector product. Distances between two manifolds.
Affine and euclidean reference systems.
Additional notes about suggested reading: Chiarellotto-Cantarini-Fiorot, Un Corso di Matematica, Libreria Progetto, Padova.

F. Bottacin, Algebra Lineare e Geometria, Ed. Escupapio, Bologna
Textbooks (and optional supplementary readings)
  • Nicoletta Cantarini, Bruno Chiarellotto, Luisa Fiorot, Un corso di Matematica. Padova: Progetto, --. Cerca nel catalogo
  • F. Bottacin, Algebra Lineare e Geometria. Bologna: Ed. Escupapio, --. Cerca nel catalogo