Linear algebra can be regarded as the theory of the vector spaces, as a vector space is a set of some objects or elements, that can be added together and multiplied by the numbers (the result remaining an element of the set), so that the ordinary rules of calculation to be valid. An example of a vector space is the geometric vector space (the free vector space), presented in the first chapter of the book, which plays a central role in physics and technology and illustrates the importance of the vector spaces and linear algebra for all practical applications. Besides the notions which operates mathematics, created by abstraction from environmental observation (for example the geometric concepts) or quantitative and qualitative research of the natural phenomena (for example the notion of number) in mathematics there are elements from other sciences. The notion of vector, brought physics has been studied and developed, creating vector calculus, which become a useful tool both mathematics and physics. All physical quantities are represented by vectors (for example the force, the velocity).