Schur complement

The Schur complement is a mathematical tool used to analyze and simplify complex matrices, often in systems of equations or optimization problems. Imagine dividing a large matrix into blocks, representing different parts of a system. The Schur complement helps determine how one part influences the other by focusing on a smaller, related matrix. It's especially useful for understanding the properties of the entire system, such as invertibility or stability, by examining these sub-components. In essence, it provides a way to condense information about a matrix’s structure and interactions, facilitating tasks like solving equations more efficiently.