 Givens rotation

A Givens rotation is the identity except for a coordinate-plane blockChoosing $(c,s)=(a,b)/\sqrt{a^2+b^2}$ maps the vector $(a,b{)}^T$ to $(\sqrt{a^2+b^2},0{)}^T$.

Givens rotation is a mathematical technique used in linear algebra for rotating vectors in two-dimensional space. It is particularly useful in the context of QR decomposition, a method for factorizing a matrix into the product of an orthogonal matrix (Q) and an upper triangular matrix (R). A Givens rotation is defined by a rotation matrix that can be constructed using two elements \( (a, b) \) of a vector or matrix.