Linear Algebra and Elements of Geometry (2006/2007)

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Teaching is organised as follows:
Unit Credits Academic sector Period Academic staff
Modulo avanzato 3 MAT/03-GEOMETRY 1° Q (seconda parte) Enrico Gregorio
Modulo base 6 MAT/02-ALGEBRA 1° Q - solo 1° anno Francesca Mantese

Learning outcomes

Module: Modulo base

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

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Module: Modulo avanzato

The aim is to introduce the first concepts of analytic and projective geometry, with elements of the theory of conic sections.

Syllabus

Module: Modulo base
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* 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.


Module: Modulo avanzato
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* Schur's Theorem and normal matrices.
* Elements of analytic geometry in plane and space.
* Elements of projective geometry of plane.
* Conic sections.

Assessment methods and criteria

Module: Modulo base
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Written test


Module: Modulo avanzato
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Written test

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