Introduction to multivariate methodology, an alternative way?

This is a tutorial for the tutor and summarises an approach to teaching the principles of principal components decomposition that apears to lower the studentʹs conceptual entrance barrier. It starts with summarising the fate of dissemination of the methodology that explains the scepticism with the methodology and defines the role distribution between expert, tutor, and student. The link of items presented are: generation of data structures, an alternative concept of correlation related to the elements of the score and loading vectors, formation of the model matrix by multiplication of the correlation vectors, interpretation of the loading vector, the latent variable, and decomposition of the centred observation matrix. One example of decomposition into three meaningful components is given, and, finally, the widespread confusion of interpreting sandwiched correlation structures is exemplified.