Givens rotation

Summary

A Givens rotation is an $n \times n$ orthogonal matrix that rotates the plane of two coordinate axes and leaves all other coordinates fixed. With the angle chosen well, it turns one chosen entry of a vector or matrix into zero. Because it touches only two rows, it is the tool of choice for zeroing single entries. This is used in the QR decomposition of sparse or structured matrices and in the QR algorithm for eigenvalues.