Koordinatenvector

A Koordinatenvektor, or coordinate vector, is a representation of a point or vector in a coordinate system. It is a list of numbers that specifies the position of the point or the magnitude and direction of the vector along each axis of the system. For instance, in a two-dimensional Cartesian coordinate system, a point P might be represented by the coordinate vector (x, y), where 'x' is the distance along the horizontal axis and 'y' is the distance along the vertical axis. Similarly, in three dimensions, a point or vector would have a coordinate vector (x, y, z). The number of components in the coordinate vector corresponds to the dimension of the space. These vectors are fundamental in linear algebra and geometry, enabling mathematical operations such as vector addition, subtraction, and scalar multiplication to be performed easily. The specific basis vectors associated with the coordinate system determine the meaning of each component in the vector. Without a defined coordinate system, a coordinate vector has no intrinsic meaning.