The scalar is a variable or function which can be expressed one number, and the material numerical value usually means. This variable does not change even if to change coordinates, unlike vectors, for example. The same vector can have them different if are in the different systems of coordinates.
Instruction
1. The abstract algebra understands a scalar as an element of the main field. Tensor calculation understands it as a valent tensor and if to replace basis of a coordinate system, it will not change. However in Newton's physics a scalar the usual scalar of space of three dimensions, energy in terms of Newton's physics – a scalar, but in terms of space and time it only consider, as a rule, a part of a four-dimensional vector.
2. The modern science considers a scalar as a variable of space and time, according to scientists it should not change during transition from one system of counting to another.
3. It is possible to give values of lengths, areas, various temperatures, masses, substance density as examples of scalars. Thus, the interpretation of a concept of a scalar depends also on a context. It is enough to tell that from a position of usual physics of several given measurements as scalar sizes are not considered at all.
4. However consider measurements which are expressed only by singular, but not being scalar sizes. For example, any coordinate of a vector can be considered as one of vector coordinates, it is not an invariant as in case the base of coordinates changes.
5. Also it is impossible to call a pseudo-scalar a scalar that can be understood even from its name. The pseudo-scalar does not change at transfer and at turn of axes of coordinates, but it changes the sign if the direction of one of axes changes on opposite.
6. People constantly deal with volumes of bodies, their masses, electric charges when studying the world around. All these characteristics of scalars register either usual Latin letters, or in figures. Scalars can also be both negative, and positive. Rules of mathematics and elementary algebra help people to make mathematical operations over scalars. However some properties of scalars cannot be described only by mathematical methods, it is necessary to resort to characteristic of these properties in temporary space.
7. The scalar is necessary for fuller understanding of space in various sciences, the scalar helps scientists to describe various measurements of natural objects in space. It is studied also at school, and higher educational institutions.