This manuscript is intended for all second year of the mathematics license students and all those who want to acquire the basic concepts of finite-dimensional endomorphism reduction written in a clear and accessible style with many examples. The content of this manuscript also includes proofs of some results.
This is the Algebra 3 course taught at the university of Abbes Laghrror Khenchela.
The object of this work is to study some processes of linear algebra which allow to simplify the description of certain endomorphisms of a vector space, in particular of certain square matrices. It consists in finding and explaining a basis of the vector space made up of eigenvectors.
Certain parts can be admitted on first reading without harming a good assimilation of new notions. The matrix trigonalization technique is given in Jordan form, following a clear and simple algorithm. His difficult demonstration is completed by a series of exercises at the end of the chapter. The diagonalization of the matrices is done by hand, without using too theoretical notions.
The content of this manuscript also includes proofs of some results. On the other hand, the examples and the exercises proposed since, we can easily construct the characteristic polynomial of matrice so that their eigenvalues.
Note that each chapter is subdivided into several sections, each of which contains a basic concepts are presented at the beginning of each section, corrected exercises, and suggested exercises. The manuscript finally ends with a chapter that we remember some definitions and present without proof the classical results on square matrices that we need in this work, and present some examinations conducted at the University of Khenchela.
In fact, these lessons, which are based on square matrices, are a continuation study of Algebra 2 taught in the first year MI.
This polycopy is organized of four chapters ordered as follows:
Firstly, the chapter 1 is devoted to explaining and studying the construction of the ring of polynomials, where we introduce preliminary results and basic theories that will be useful in studying the Reduction of endomorphisms of finite-dimensional vector spaces.
- معلم: lamia Djebara