Orthogonalization
Orthogonalization is a mathematical process used to transform a set of vectors into a new set that are mutually perpendicular, or orthogonal, to each other. This is important in various fields, such as linear algebra and statistics, as it simplifies calculations and helps in understanding the structure of vector spaces. The most common method for orthogonalization is the Gram-Schmidt process, which systematically adjusts the vectors to ensure they are orthogonal.
In practical applications, orthogonalization is often used in machine learning and signal processing to improve the performance of algorithms. By working with orthogonal vectors, computations become more efficient, and issues like multicollinearity in regression analysis can be mitigated. This leads to clearer interpretations and better model performance.