- Docente: Michele Mulazzani
- Credits: 6
- SSD: MAT/03
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
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Corso:
First cycle degree programme (L) in
Environmental Engineering (cod. 9198)
Also valid for First cycle degree programme (L) in Civil Engineering (cod. 8888)
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from Sep 18, 2024 to Dec 19, 2024
Learning outcomes
Basic topics of matrix and vector calculus; in particular: computation of determinants, matrices inverses, linear systems, eigenvalues, eigenvectors and eigenspaces of matrices.
Course contents
Linear systems.
Algebraic structures. Standard operation on K^n. Linear
systems.
Matrices.
Basic definitions. Matrix algebra. Linear systems and
matrices.
Vector spaces.
Basic definitions. Subspaces. Linear combinations. Sum of
subspaces.
Bases.
Linear dependence. Bases and dimension. Rank of matrices.
Application to linear systems.
Linear transformations.
Linear transformations. Isomorphisms and endomorphisms. Imagine
and Kernel of linear transformations.
Matrix representation of linear
transformations.
Matrix representation of linear transformations and endomorphisms.
Bases change formula.
Determinants.
Permutations. Determinants. Properties of determinants. Laplace
formula. Inverse matrix. Applications to computation of rank.
Applications to linear systems.
Rappresentation of subspaces.
Cartesian and parametric representation of subspaces.
Eigenvalues, eigenvectors and eigenspaces.
Eigenvalues, eigenvectors and eigenspaces of endomorphisms and
matrices. Matrix similarity. Characteristic polynomial.
Diagonalization of matrices.
Bilinear and quadratic forms.
Bilinear forms. Matrix representation of bilinear forms. Matrix
congruence. Index. Real quadratic forms. Canonical forms. Euclidea products, orthonomal bases, Gram-Schmidt algoithm.
Readings/Bibliography
M.R. Casali, C. Gagliardi, L. Grasselli, "Geometria", Esculapio,
Bologna, 2016.
A. Cattabriga, M. Mulazzani, "Prove d'esame risolte di Geometria e
Algebra per i corsi di laurea in Ingegneria", Esculapio, Bologna,
2015.
A. Barani, L. Grasselli, C. Landi, "Algebra lineare e Geometria -
Quiz ed esercizi commentati e risolti", Esculapio, Bologna,
2014.
L. Gualandri, "Algebra lineare e Geometria. Esercizi e quiz
risolti e d'esame", Esculapio, Bologna, 2007.
Teaching methods
Lessons on blackboard
Assessment methods
See
http://www.dm.unibo.it/~mulazza/didattica.htm
Teaching tools
See
http://www.dm.unibo.it/~mulazza/didattica.htm
Links to further information
http://www.dm.unibo.it/~mulazza/didattica.htm
Office hours
See the website of Michele Mulazzani