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

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Course code
4S00253
Name of lecturer
Enrico Gregorio
Number of ECTS credits allocated
3
Academic sector
MAT/03 - GEOMETRY
Language of instruction
Italian
Location
VERONA
Period
First term (second part) dal Dec 11, 2006 al Dec 21, 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.
* Elements of analytic geometry in plane and space.
* Conics and quadrics.

Assessment methods and criteria

Written test

Teaching aids

Documents