The one of vectorial space is a concept inherent to the branch named as abstract algebra, which is the part of the math that takes care of study of algebraic structures, such as groups, bodies, and vector spaces , which are precisely the subject of this review.
Now, it is important before entering into the concrete concept of vector space to discover what a vector, which is precisely the element of these structures ...
The vector is a geometric instrument that is used for represent a physical quantity which will be determined by its length, orientation and direction. Geometrically they are represented from line segments that go to a certain side, similar to an arrow. Examples of the most common vector quantities include the force that is exerted on a certain object and speed to move displayed by a mobile.
All physical systems have some measurable qualities, which are precisely the magnitudes. Although we can find those quantities that do not need to know the aforementioned aspects of direction sense, orientation and length for their definition, there are others, such as those indicated for speed and force, that do require it.
It should be noted that on vectors it is feasible to perform basic mathematical operations such as: addition, subtraction, division and multiplication.
Having clarified the concept of vector, we will move on to that of vector space ...
The vector space, then, is a algebraic structure originated from sets whose elements are plausible to be added together and multiplied by numbers. A vector space is always linked to a set that will have a body structure and elements called scalars, which will act as numbers. Meanwhile, the elements of the vector space will be represented by the vectors.
