Hi, X is a n x p matrix, V is a linear transformation (p x q with q<=p) and Y = XV (n x q). If V is formed by the eigenvectors of the covariance matrix of X, then :
sum(var(y_i)) = sum(var(x_j)) i=1..q, j=1..p I understand that it is this theorem that enables us in PCA to say that var(y_1)/sum(var(y_i)) can be interpreted as the percentage of explained variation by the factor 1. If sum(var(y_i)) does not equal sum(var(x_j)) (the "aggregated variance" in the original x-space), it is not possible anymore to interpret the ratio as the % of explained variation. Am I right? So my question is : if V is a general linear transformation with v_i * v_i' = 1 (where ' denotes the transpose and i = 1..q) but not the eigenvector matrix, not even orthogonal (so the matrix does not qualify as a rigid rotation of the axes), is there a way to express the percentage of explained variation by the "factor" 1? Any hint is appreciated, Patrick . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
