Linear Algebra (2011/2012)

Course code
4S00002
Name of lecturer
Enrico Gregorio
Coordinator
Enrico Gregorio
Number of ECTS credits allocated
6
Other available courses
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Period
I semestre dal Oct 3, 2011 al Jan 31, 2012.

Lesson timetable

I semestre
Day Time Type Place Note
Tuesday 10:30 AM - 12:30 PM lesson Lecture Hall Gino Tessari  
Wednesday 3:30 PM - 4:30 PM lesson Lecture Hall Gino Tessari  
Thursday 10:30 AM - 12:30 PM lesson Lecture Hall Gino Tessari  

Learning outcomes

Introduction to the fundaments of Linear Algebra with some applications.

Syllabus

* Matrices and linear systems: matrices, operations on matrices, systems of linear equations, Gauss elimination, inverses of matrices, LU factorization.
* Vector spaces: definition and examples, subspaces, generators. Linearly dependent and independent vectors, bases, dimension.
* Linear maps and associated matrices: composition of linear maps and matrix multiplication, change of basis, kernel and image of a linear map, rank of matrices, dimension formula.
* Inner products and orthogonality: inner product of vectors, orthogonal and orthonormal bases, orthogonal projections, Gram-Schmidt algorithm.
* Canonical forms: eigenvalues and eigenvectors, characteristic polynomial, algebraic and geometric multiplicity, diagonalizability criteria.

Assessment methods and criteria

Written test