But m_y = 0, the covariance of Y is then
E(YY^T) = L = E{[C(X-m_x)][C(X-m_x)]^T}
L = CE[(X-m_x) (X-m_x)^T]C^T             (4)
L = CåC^T
where å is the (p x p) covariance matrix of x-variables and L is the covariance matrix of uncorrelated of y-variables.

L is a diagonal matrix which the elements are eigenvalue of x - variables. The first three eigenvectors which the higher variance will be selected to create the principal component images. These three images will assigned by the colour of R, G and B to create a colour composite of PCA image.

Here, 6 images from thermatic mapper system of Landsat in Fig. 1 have been used in PCA process. The corresponding 6 components from PAC are shown in Fig. 2. the colour image obtained by first three components is presented in Fig. 3. This colour image contains the 95 percents of the total variance.

Fig. 1 Original images



Fig. 2 Six component images from PCA



Fig 3 PCA colour image contained 95 percents of the total variance
(PC1 = red, PC2 = green, PC3 =blue)