Vector, also known as vector, was originally applied to physics. Many physical quantities such as force, velocity, displacement, electric field intensity and magnetic induction intensity are vectors. Around 350 BC, Aristotle, a famous ancient Greek scholar, knew that force can be expressed as a vector, and the resultant force of two forces can be obtained through the famous parallelogram rule. The word "vector" comes from directed line segments in mechanics and analytic geometry. Newton, a great British scientist, was the first to use directed line segments to represent vectors.

The vector discussed in the textbook is a quantity with geometric properties. In addition to the zero vector, you can always draw an arrow to indicate the direction. However, there are more vectors in advanced mathematics. For example, if all polynomials with real coefficients are regarded as a polynomial space, the polynomials here can be regarded as a vector. In this case, it is impossible to find the starting point and the ending point, or even draw an arrow to indicate the direction. The vectors in this space are much wider than those in geometry. It can be any mathematical object or physical object. This can guide the application of linear algebra method to a wide range of natural science fields. Therefore, the concept of vector space has become the most basic concept in mathematics and the central content of linear algebra, and its theories and methods have been widely used in various fields of natural science. Vector and its linear operation also provide a concrete model for the abstract concept of "vector space".

Judging from the history of mathematical development, the vector structure of space has not been recognized by mathematicians for a long time in history. It was not until the end of 19 and the beginning of the 20th century that people linked the nature of space with vector operation, making vector a mathematical system with excellent universality of operation.

Vector can enter mathematics and develop, first of all, we should start with the geometric representation of complex numbers. At the end of18th century, wiesel, a Norwegian surveyor, first expressed the complex number A+Bi with points on the coordinate plane, and defined the vector operation with geometric complex operation. Points on the coordinate plane are represented by vectors, and the geometric representation of vectors is used to study geometric problems and trigonometric problems. People gradually accepted complex numbers and learned to use them to represent and study vectors on the plane.

But the use of complex numbers is limited, because they can only be used to represent planes. If there are forces that are not in the same plane acting on the same object, we need to find the so-called three-dimensional "complex number" and the corresponding operation system. /kloc-In the middle of 0/9th century, British mathematician Hamilton invented quaternion (including quantity part and vector part) to represent vectors in space. His work laid the foundation for vector algebra and vector analysis. Subsequently, the electromagnetic theory was established.

The initiation of three-dimensional vector analysis and the formal division of quaternion were independently completed by Gubbs and Hiveside in Britain in the 1980s of 19. They put forward that vector is only the vector part of quaternion, but it is not independent of any quaternion. They introduced two kinds of multiplication, namely product and cross product of quantities, and extended vector algebra to vector calculus with variable vectors. Since then, vector method has been introduced into analytical and analytic geometry.