I have various object vectors (PC1, PC2, PC3) representing objects ater normalisation and PCA. I also have 'axis' vectors (PC1, PC2, PC3) representing the axis that the objects were originally placed along e.g. hot/cold, like/dislike. What I would like to know is if I do a projection of the object vectors on to the 'axis' vectors does this effectively give a representation of the original (normalised for all datasets) data? Can I then take object-axis projections for many entries to give average and s.d. values?
I add that the PCA and normalisation was done with multiple entries for the same bunch of objects and axis i.e. 20 people x 16 objects x 5 description axis (but description axis considered seperately i.e. vectors all different). Unfortunately it was also done in software which is rather black box in what it does (please dont just tell me to use something else though).