Stepwise Givens rotation
A Givens rotation acts only in one coordinate plane, leaving the remaining coordinates unchanged. This makes it a precise geometric tool for zeroing one chosen entry at a time while preserving orthogonality. The active vector is rotated just enough so that one selected component becomes zero, and repeating that idea systematically transforms the matrix toward upper triangular form. In QR factorization, the transformed matrix becomes the triangular factor, while the accumulated rotations produce the orthogonal factor.
