unitnormalized

Unitnormalized is an adjective used to describe something that has been scaled to unit length. In mathematics and computer science, unit normalization refers to converting a vector or set of vectors so that their length equals one. For a nonzero vector v, the unit vector in its direction is v_hat = v / ||v||_2, where ||v||_2 is the Euclidean (L2) norm. This process is commonly known as L2 normalization. Other norms can yield unit length as well, such as L1 normalization, which scales so the sum of absolute values equals one, or L∞ normalization, though unitnormalized typically implies L2 normalization.

When applied to matrices, unit normalization can be performed on rows or columns, depending on the application. In data processing and machine learning, unitnormalization helps reduce the impact of differing magnitudes across features and is often used with cosine similarity, which depends on vector direction rather than length. In software, a unitnormalized vector is one that has been scaled to have length one; if the input vector is zero, implementations may return the zero vector or apply a small epsilon to avoid division by zero.

The term is commonly encountered in libraries or documentation to indicate that a vector or feature has been scaled to unit length. It is distinct from centering data or adjusting variance; unit normalization concerns length, not mean or dispersion. A unitnormalized vector represents a direction with unit magnitude, enabling comparisons of orientation such as angles and cosine similarity.