Matrix Analysis, April 4-29, 2005

Professor Eric Lehman
University of Caen, France

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Description of content
Matrix analysis is the simplest way to combine linear algebra with the properties of real and complex numbers. It is the basic mathematical tool in all branches of applied mathematics. The course will develop mainly three aspects:
- analytic functions of a matrix, like exp(A), needed to solve systems of linear differential equations, or formulae like:

(I -A)-1 =  ¥ å n = 0 An

- normal matrices, including hermitian, unitary and orthogonal matrices
- singular value decomposition, applied to matrix approximation problems and to stability of dynamical systems.

Recommended pre-knowledge
Elementary computations with matrices: sum, linear combination and product of matrices, inverse, eigenvalues and eigenvectors of a matrix.

20 hours lectures/exercises + exam or seminar presentation (2 credits)

 

Tentative meeting schedule
Weeks 10-13

Date	Time	Place
Monday 4.4., 11.4. and 18.4.	12-15	M6
Wednesday 6.4. and 13.4.	14-16	M8
Thursday 7.4. and 14.4.	12-14	M10
Monday 25.4.	12-16	M18 (computer lab)

Note: passing this course gives 1 credit of the English language studies (in "common studies" of the Faculty of Science)