GEOMETRY B
cod. 14003

Academic year 2007/08
3° year of course - First semester
Professor
Academic discipline
Geometria (MAT/03)
Field
A scelta dello studente
Type of training activity
Student's choice
36 hours
of face-to-face activities
4 credits
hub:
course unit
in - - -

Learning objectives

<br />We will study Linear Algebra and its applications, in particular to Geometry in the space.<br /> 

Prerequisites

Geometria A

Course unit content

<br /><br />Linear maps and matrices in the euclidean plane: projections, reflections, rotations, isometries. Group theory. Real and complex vector spaces.<br />Linear maps: kernel and image, the dimension's formula. Basis change and matrices. Matrices of linear maps on finite dimensional vector spaces.<br />Invariant subspaces, eigenvalues, eigenvectors. Diagonalization of operators. Orthogonal matrices and operators. Systems of ordinary differential equations with constant coefficients.<br />Bilinear forms and scalar products. Spectral theorem. Diagonalization of symmetric matrices using orthogonal matrices. Classification of quadric surfaces in the space.

Full programme

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Bibliography

<br />M.Artin, Algebra, Bollati-Boringhieri 1997.

Teaching methods

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Assessment methods and criteria

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Other information

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