Gram-Schmidt Orthogonalization Algorithm

The Gram-Schmidt Orthogonalization Algorithm is a method used in linear algebra to take a set of vectors and transform them into a new set that is orthogonal, meaning each vector is perpendicular to the others. This is useful in various fields, including computer science and physics, for simplifying calculations and improving accuracy. The process involves adjusting each vector to eliminate any overlap with the previously adjusted vectors, ensuring they are mutually perpendicular while retaining the original span of the vector space. The resulting orthogonal vectors can then be used for simplifying problems involving projections and transformations.