Title of the course: Matrix eponential
Instructor: Prof. Adrien Deloro
Institution: Sorbonne Université
Dates: 19-24 July 2021
Prerequisites: Analysis: real and complex numbers; series, convergent and absolutely convergent series; Cauchy sequences
Linear algebra: vector spaces, norms on finite-dimensional vector spaces, matrices, matrix algebra; diagonalisation and trigonalisation
Level: 3rd/4th year
Abstract: The real/complex exponential is central in studying differential equations; for systems of linear differential equations, the matrix exponential (yes, exp of a matrix) plays the same role.
We shall define it and study its algebraic and analytic properties; attention will be paid to how to compute it effectively. Last, we’ll apply it to systems of differential equations. Time permitting, there will be more applications to the study of G(n, C).
Knowledge of ODEs is not required but familiarity with linear algebra is.
Language: EN