Linear Algebra and Elements of Geometry - modulo di base (2007/2008)

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Course code
4S00253
Name of lecturer
Francesca Mantese
Number of ECTS credits allocated
6
Other available courses
Academic sector
MAT/02 - ALGEBRA
Language of instruction
Italian
Location
VERONA
Period
1° Q - solo 1° anno dal Oct 15, 2007 al Nov 30, 2007.
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To show the organization of the course that includes this module, follow this link * Course organization

Lesson timetable

Learning outcomes

The aim is to introduce the basic facts about Linear Algebra and its applications

Syllabus

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

Reference books
Author Title Publisher Year ISBN Note
E.Gregorio, L.Salce Algebra Lineare Libreria Progetto Padova 2005

Assessment methods and criteria

Written test

Teaching aids

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