Monday, September 22, 2014
nD Rotation Matrices
It's possible to find a matrix that will rotate a vector in a plane a given angle in n-space. To show this in 4D we choose two arbitrary unit vectors, a and b, to define the plane and make the second perpendicular to the first. Next we pick a unit vector, x, in the plane obtained by rotating the vector a by α = 5 degrees. The vector y is perpendicular to x in the ab-plane. We can find another vector, x', by rotating x and angle β in the plane using the formula found previously. The matrix R(α) shown below performs the same rotation as shown by the result x''.
The matrix used will rotate any vector in the plane 10 degrees in the same direction.