I know that you want to use principal component analysis when you believe that the independent variables are correlated with each other. But someone told me that if you do not have enough data, it is not worth it, and I do not really know why.
My current data has about 80 rows and 17 columns, so 80 observations and 17 independent variables. Is it good to use?
PCA only gives useful results when the independent variables are correlated with each other. There are guidelines, such as having at least 5 observations per variable, but these are not followed widely in practice, as they tend to be based on some pretty heroic assumptions. In particular, if there is a very clear structure in your data with a small number of components then having 80 observations for 17 variables is find, but if the structure is not clear, then your result is likely to be pretty unstable. You can find lots of references and related discussion in the answers to this question.
