Given a matrix , the rotation matrix with , zeroes the position of the matrix. For an upper Hessenberg matrix of order n, let
Then , an upper triangular matrix. This generates the QR decomposition of .
matrix 
, the rotation matrix
with 
, zeroes the
position of the matrix. For an upper Hessenberg matrix
of order n, let
, an upper triangular matrix. This
generates the QR decomposition of 
.