Hamilton weather forecast

Vector can be seen everywhere in daily life, and it should be the basic knowledge of mathematics that future citizens should know. For example, the weather forecast mentioned that "the wind force is level 3, and the wind direction is northeast", which has two factors: size and direction. As for the position vector, it involves two parts: distance and direction. The sum of the thrust of the river and the power of the ship is represented by the vector diagram contacted by the primary school. In mathematics, points are usually used to indicate position and rays are used to indicate direction. In a plane, all rays from any point can be used to represent all directions in the plane. Representation of vectors The representation of vectors is usually represented by directed line segments. The length of the directed line segment indicates the size of the vector, and the direction pointed by the arrow indicates the direction of the vector. Vectors can also be represented by letters a, b, c, etc. , or use letters to indicate the starting point and ending point of the directed line segment of the vector. The size of the vector, that is, the length (or modulus) of the vector is recorded as |a| A vector with a length of 0 is called a zero vector, and a vector with a length equal to 1 unit length is called a unit vector.

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 British scientist, was the first to use directed line segments to represent vectors. Research shows that the vector used in daily life is a quantity with geometric properties. In addition to the zero vector, you can always draw an arrow to indicate the direction. But there are wider vectors in higher 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 vector in this space is much wider than that in geometry, and it can be any mathematical object or any physical object. In this way, it can guide the application of linear algebra method in a wide range of natural sciences. 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 entered mathematics and developed at the end of18th century. Wiesel, a Norwegian surveyor, first expressed the complex number A+Bi by points on the coordinate plane, and defined the vector operation by using the 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 the complex number and learned to use it to represent and study the vector on the plane, so the vector quietly entered mathematics.

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 the vector of space. His work laid the foundation for the establishment of vector algebra and vector analysis. Subsequently, Maxwell, the discoverer of electromagnetic theory and British mathematical physicist, treated the quantity part and vector part of quaternion separately, thus creating a large number of vector analysis.

The creation 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 suggest that a vector is only the vector part of quaternion, but it is not independent of any quaternion. They introduced two kinds of multiplication, namely quantity product and cross product. Vector algebra is extended to vector calculus with variable vectors. Since then, vector method has been introduced into analytical and analytic geometry, and gradually improved, becoming an excellent mathematical tool.