Linear Algebra and Elements of Geometry - Modulo base (2006/2007)

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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
1st quadrimester (only for 1st year of 3-year degree courses) dal Oct 23, 2006 al Dec 1, 2006.

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 dependendency and independency, 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.

Assessment methods and criteria

Written test

Teaching aids

Documents