Hi! When a reduce the dimension of the data using PCA, can I say that the first priniciple component refers to the first element, the second to the second and so on? thanks in advance!

What do you mean by "element"? The first principle component is the axis of most variation. If you're talking about the elements of the data set, then no, not at all.

ok, thanks!
but let's say have have this data
(the rows are the experiments and the columns are the things we check in the experiments.):

a1, b1, c1, d1, e1, f1
a2, b2, c2, d2, e2, f2
a3, b3, c3, d3, e3, f3
a4, b4, c4, d4, e4, f4

and I have the principle components.
Is there any way to know which of the "checked things" had the greatest impact?
can I know if the b's are the most effective ones?

The components that arise from PCA are linear combinations of the orignal data. As Sneftel said, the first principle component is essentially the axis of maximum variation withint your data. The result is that you're rotating your data to a new set of axes in which the "first" axis has the maximum variation. The second component/axis has the second most variation with the additional constraint that it is orthogonal to the first. All subsequent components are orthogonal to all those found thus far.

Most PCA tools give you a set of loadings or the equations (or matrix) used to generate the components. You can investigate this matrix to see which columns of original data have the highest coefficients for any particular axis suggesting that they are the most influential. You could also do a crude estimation by checking the correlation between your original data columns and the new PCA columns/components. The orginal column with the highest correlation to a particular component must be influencing it the most. Be careful with either of these method and look for large differences. If you have one correlation at .85 and another at .83, I'd say they are equally influential.

-Kirk

ok, thanks!
I'll check it out.