Contact Sheet
Prof of the Courses : Dr. Abdelmadjid Djehiche
Contact: by email at djehiche.a@centre-univ-mila.dz
Target audience: 1st year License Science and Technology
Course title: Algebra 2
Credit: 04
Coefficient: 02
Duration: 12 weeks/Course:1h30,
/Tutorial session: 1h30
Schedule: Thursday: 09:00 a.m. - 11:00 a.m.
Lecture hall: A02
Abstract
This course in Algebra II introduces the fundamental concepts of vector spaces, emphasizing their essential role in understanding dimensions, basis vectors, and coordinate representations. Particular attention is devoted to linear transformations and their relationship to changes of coordinates and bases, providing a coherent framework for interpreting transformations within vector spaces. These topics are developed in Chapter 1.
Chapter 2 focuses on matrices, a central tool in engineering and applied mathematics for representing and manipulating multiple numerical or functional quantities. The intrinsic connection between matrices and linear transformations is explored in order to establish a deeper and more unified understanding of matrix theory. Key matrix operations and properties, including determinants, transposes, and inverses, are also examined.
In Chapter 3, matrices are applied to the resolution of systems of linear algebraic equations, highlighting their practical importance in solving complex problems.
The final chapter is devoted to eigenvalues and eigenvectors. The objective is to study linear transformations from a vector space to itself in order to simplify matrix representations, particularly through diagonalization or reduction to canonical forms, thereby facilitating both theoretical analysis and practical computations.
Prerequisites
The basic notions of mathematics and algebra 1(groups, fields, linear transformations...).Contents
Chapter 1: Vector spaceschapter 2: Matrix algebraChapter 4: Eigen values and eigen vectors