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Matematics and Operation research

Corso di laurea magistrale in
MULTIMEDIA SIGNAL PROCESSING AND TELECOMM. NETWORKS

Academic year 2012-13                 Prof F. Odetti - Prof. A.M. Rossi

 Program    Texts  
 Diary of lessons of the part of this course concerning linear algebra and geometry  

Prerequisites: Linear algebra: matrices, linear systems, gaussian elimination.
Vector spaces: Subspaces, linearly independent vectors, generators (spanning sets), bases, dimension.
Diagonal form of a matrix: eigenvalues, eigenvectors, eigenspaces.
Scalar products. Orthogonal vectors. Orthonormal bases. Orthogonal matrices.
Spectral theorem (symmetric matrices are diagonalizable). Quadratic forms.
Analytic geometry of plane: conic sections.
Analytic geometry of space: lines, planes, distances, circles, spheres.


An outline of the program is the following:

References:

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Lessons of geometric and algebraic part (prof. F.Odetti)

Thursday 09/27/2012

Thursday 10/04/2012 Tuesday 10/9/2012 Thursday 10/18/2012 Thursday 10/25/2012 Thursday 11/8/2012 Thursday 11/15/2012 Thursday 11/22/2012

Theory notes

Outline of theory. First part: Orthonormal bases, norms and condition number: 7 pages Sep 27, 2013
Outline of theory. Second part: Changes of coordinates, curves, surfaces, quadrics 8 pages Nov 5, 2012

Exercises (with many answers)
Warning: These notes are under further development:
A new version will be ready in a few weeks

Exercises on Orthonormal bases, norms and condition number 2 pages Dec 23, 2012
Answers to Orthonormal bases, norms and condition number 3 pages (for now) Dec 23, 2012
Exercises on Changes of coordinates, curves, surfaces, quadrics 5 pages Dec 23, 2012
Answers to Changes of coordinates, curves, surfaces, quadric 6 pages (for now) Dec 23, 2012

Remark: Many answers are still missing. Possibly there are errors.
Comments and notifications of errors shall be welcome.
At the bottom of each page you'll find the date of release.

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