The aim of giving this course is to familiarize the student with a great deal of important and comprehensive topics, from which he will benefit greatly in other courses after passing this course. Among the general objectives that the student acquires after successfully completing the course is his study of vectors and their properties, as well as his study of vector spaces, vector space conditions, and knowledge of subspace , and proving some related theories, knowing the concept of linear structure, correlation, linear independence, the generated group, knowing the concept of base and dimension, as well as learning about linear transformations and the internal multiplication space and its properties, and comparing eigenvalues and eigenvectors, and being able to link all the skills and experiences he learned from This course is similar to other skills in other locations.