Solomon's theorem

Solomon's theorem, in mathematics, states that if you have a set of objects with certain relationships, the total number of these relationships can be determined by considering how they interact in pairs. Specifically, when working with linear relationships in algebra or systems of equations, the theorem helps establish that the sum of the ranks of combined systems minus the ranks of individual systems equals the rank of their union. This principle is useful in areas like combinatorics and linear algebra for understanding how different parts of a system relate and overlap, ensuring a clear understanding of the structure and dependencies within the entire system.