Whenever two Series or DataFrames operate with another Series or DataFrame, the indexes (both the row index and column index) of each object align first before any operation begins. This index alignment happens silently and can be very surprising for those new to pandas. This alignment always creates a Cartesian product between the indexes unless the indexes are identical.
A Cartesian product is a mathematical term that usually appears in set theory. A Cartesian product between two sets is all the combinations of pairs of both sets. For example, the 52 cards in a standard playing card deck represent a Cartesian product between the 13 ranks (A, 2, 3,..., Q, K) and the four suits.
