egységvektornormálás

Egységvektornormálás, also known as vector normalization, is a process in linear algebra where a vector is scaled to have a unit length, i.e., its magnitude becomes 1. This is achieved by dividing each component of the vector by its magnitude. The formula for normalizing a vector v = (v1, v2, ..., vn) is given by:

v' = (v1/magnitude, v2/magnitude, ..., vn/magnitude)

where magnitude is the length of the vector v, calculated as:

magnitude = sqrt(v1^2 + v2^2 + ... + vn^2)

The resulting vector v' is called the unit vector or normalized vector. Normalization is a common operation in various fields such as computer graphics, machine learning, and physics. It is particularly useful when the direction of a vector is more important than its magnitude, or when comparing vectors of different lengths. For example, in computer graphics, normalization is used to calculate the direction of light rays or the direction of a camera's view. In machine learning, normalization is used to scale features to a similar range, which can improve the performance of algorithms.