Oates Theorem

Oates’ Theorem concerns the solution of certain systems of linear equations, specifically those involving matrices with specific properties. It states that for a system of linear equations, if the matrix involved is positive definite (meaning it has nice mathematical properties like all positive eigenvalues), then the system has a unique solution. This theorem is fundamental in fields like optimization and statistics because it assures that solutions are well-defined and stable when dealing with such matrices. Essentially, it guarantees that under these conditions, the equations won't have ambiguous or non-existent solutions.