Elementary Linear Algebra

The present book is an English translation from my book with the same title in the Arabic language which is based on my lectures given to students of various colleges studying mathematics. This edition of Elementary Linear Algebra gives an introductory treatment of linear algebra that is suitable for a first undergraduate course. Its aim is to present the fundamentals of linear algebra in the clearest possible way. The author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches.This book consists of seven chapters. Chapter 1, " vector spaces" Chapter 2 contains the " Euclidean spaces". In Chapter 3, we will discuss " The Determinant" as a practical part and very useful in Linear Algebra. Chapter 4 presents " Linear Transformations" which a fundamental part, and has many applications. Chapter 5, contains " Eigenvalues and Eigenvectors". Chapter 6 contains " Linear transformations in normed spaces.