PCA / FA malinowski: example 5. target testing

Recall that we computed the SVD of this matrix:

and we found that the w matrix was

Because w has only two nonzero entries, we know that X is of rank 2. Its three columns only span a 2D space.

Given a column of data x (a variable, in this example, of length 5), Malinowski wants to know if it is in that 2D space. As he puts it, “if the suspected test vector [x] is a real factor, then the regeneration will be successful.” He gives us a formula for computing t; by a successful regeneration, he means that is close to x.