You are supplied with a sequence of motion capture data obtained by filming a person walking. The data comprises 10 joint angles (each expressed as Euler angles, i.e. degrees of rotation about X, Y and Z axes). The sequence comprises 500 samples of these joint angles captured over a short time.

(i) Describe the mathematical steps required to perform principal component analysis (PCA) on this data. State the dimensions of any matrices used in your equations.

(ii) You wish to produce a plot visualising variation in the data. How can you use the results of the PCA to do this? Include equations in your answer, as appropriate.

(iii) 3 joints are moving independently in the sequence. What might you observe about the values in V?