Vectors. Concepts and sum of vectors

Vectors are fundamental mathematical entities in the fields of geometry and linear algebra. A vector is any mathematical entity that can be represented by an oriented line segment.

Mathematically, a vector is represented by a letter with an arrow on top. Graphically, it is represented by an arrow in n-dimensional space, where each component of the vector represents a quantity in a specific direction. Thus, a vector is defined as a sequence of ordered numbers. For example, a two-dimensional vector can be represented as (x, y), where “x” is the component on the x-axis and “y” is the component on the y-axis. In a three-dimensional space, the vector is represented as (x, y, z), where “z” is the component on the z-axis. Different operations can be performed with vectors, such as addition, subtraction, multiplication by a scalar, scalar product and vector product.

Vectors are widely used in physics, engineering and many other scientific disciplines. They are used to represent physical quantities with direction and modulus, such as forces, velocities and displacements. They are also useful in image processing, artificial intelligence and machine learning, where they are used to represent characteristics or attributes of data. Their study and understanding make it possible to model physical phenomena and solve problems in various fields, which makes them a fundamental tool in the analysis and representation of data and phenomena in the real world.