What is tensor?

What Does tensor Mean

Tensor is a term that can be used as an adjective or as a noun . In the first case, it refers to what causes or can produce tension .

When used as a noun , the notion of a tensor can refer to different issues. At a general level, the term refers to what is used with the aim of tensing something . For example: “The storm destroyed a bridge tensioner and traffic had to be interrupted” , “Experts indicated that the tower collapsed due to the poor condition of the tensioner” , “We have not yet received the tensioners to install the antenna and be able to start with the transmissions ” .
As can be seen in one of the examples in the previous paragraph, this concept is related to bridges , specifically to pendants, which take advantage of the great resistance capacity of steel cables to withstand constant traction. In short, suspension bridges have two or more support towers that are located at a certain distance from each other, enough so that the road or a section of it is placed between them, and have the purpose of transmitting loads to the foundation soil.

With regard to the materials and geometric shapes of the support towers , there is a great variety; They are generally founded on reinforced concrete, to resist constant contact with the earth and water, and have a steel or wood superstructure, among other possibilities. In its upper part the main cables are placed, which extend from the base of one tower to that of the next; They must be made of highly resistant steel, since they will have to withstand almost all the loads that the bridge receives.
Between one tower and another, and from each main cable, many tensioners must be suspended, at equal distances from each other and oriented vertically; They can be cables with a diameter smaller than the main ones, or iron rods that are screwed into the tip. Between each tensioner there is usually an average distance of 5 meters. From its base hang transverse elements, steel beams or other materials, which cross the width of the bridge structure. In the same way, they support other girders along the bridge, which serve to interconnect all the tensioners.
One of the best known suspension bridges is the Golden Gate , which translates as Golden Gate , located in the San Francisco Bay of the state of California, United States. Its imposing appearance and its characteristic red color appears in countless North American films, for which it has become one of the symbols of the country worldwide.
For geometry , a tensor is an entity composed of several magnitudes that depend on the coordinates. The values ​​of the tensor vary according to the coordinate system that is chosen.

In physics , on the other hand, the system formed by magnitudes of the same nature and that coexist is called a tensor. These magnitudes, in this way, can be ordered in columns and in rows like the elements that are part of a matrix ; therefore, the same rules can be applied to them as for matrix calculations.
To understand what a tensor is for geometry and physics, it is necessary to know that quantities have different categories according to the degree of freedom (that is, the smallest number of real numbers that are needed for the complete determination of the state ). We can differentiate between scalar quantities (whose representation can be made with a single number), vector-type quantities (several numbers are needed) and quantities in a quadratic form (they need a matrix with different indices).
Whereas scalar quantities and vectors are specific cases of tensors, quantities of quadratic form can only be thought of as tensors. The number of indices that distinguishes between scalars, vectors, and tensor quantities is called the tensor range .

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