The PCA equation

The PCA method is a bilinear technique which express a data matrix as a matrix product of two matrices:

$\displaystyle {\bf X} = {\bf T}{\bf P}^{T} + {\bf E}$    

where both the scores ($ {\bf T}$) and the loadings ($ {\bf P}$) matrix are orthogonal (the loading matrix vectors are also orthonormal). Thus:

$\displaystyle {\bf t}_i^{T}{\bf t}_j$ $\displaystyle = 0, \forall i \neq j$    
$\displaystyle {\bf p}_i^{T}{\bf p}_j$ $\displaystyle = 0, \forall i \neq j$    

in addition $ {\bf p}_i^{T}{\bf p}_i = 1$.



Bjørn Kåre Alsberg 2006-04-06