A Givens rotation  represents a rotation in a plane represented by a matrix of the form
where the intersections of the th and th columns contain the values and . Multiplying a vector by a Givens rotation matrix represents a rotation of the vector in the plane by radians.
According to Wikipedia, the main use of Givens rotations in numerical linear algebra is to introduce zeros in vectors or matrices. Importantly, that means Givens rotations can be used to compute the QR decomposition of a matrix. An important advantage over Householder transformations is that Givens rotations are easy to parallelize. Continue reading