This paper presents a model for teaching vector orthogonal rotation with the use of a computer-aid statistical graphics software. The rotation transformations are defined as: x’ = x cosθ + y sinθ and y’ = -x sinθ + y cosθ. The purpose is to facilitate students’ understanding of a rotation matrix by allowing them to explore and plot different values of theta (θ) given a point P. Students will learn that the maximum variance is reached when θ = 45 degrees. They will also examine the graphical and statistical properties of these transformations, in particular that the variability along y’ is the largest and that x’ and y’ are uncorrelated (orthogonal). Finally students explore how to determine the angle theta so that the variability of a set of observations along the y’ axis is maximized and x’ is orthogonal to y’.
(Monday 14th, 16:15-17:45) In session C4B
Jaime Curts (United States)