following matrix is the two dimensional Givens Rotation from the axis to the axis:
matrix rotates two dimensional column vectors about the origin of the - plane.
instance, if we rotate the unit column vector using this Givens Rotation, then we have:
if we rotate the column vector , then we have:
to rotate that column vector back to the axis so that the value is zero, we would have:
we need to use an angle such that the value goes to zero. Let’s concentrate on that lower equation:
atan2( y, x ) in C/C++ and
ArcTan[ x, y ] in Mathematica.
when we rotate the column vector back to the axis so that the value is zero, we have:
the radius from the origin to the column vector is (also known as the norm), then we also have: