Here are the original faces:

Subtracting the average (arithmetic mean) face gives us zero-mean faces:

From the original faces we compute 16 eigenfaces:

Using the eigenfaces as "basis", the closest match for the original faces is:

Now we take a test face, , we subtract the average face to obtain , and look at it in the eigenbasis: The coordinates of the test face happen to be closest to the coordinates of the 2nd original face.

Now we take another test face, namely the 2nd original face flipped upside down, , again subtract the average face to obtain , and look at that in the eigenbasis: The coordinates of that test face happen to be closest to the coordinates of the 10th original face. This shows how the method doesn't handle rotations.

Now we take another test face, namely the 2nd original face rotated 180 degrees, , again subtract the average face to obtain , and look at that in the eigenbasis: The coordinates of that test face happen to be closest to the coordinates of the 12th original face. This shows how the method doesn't handle rotations.