A History of the Development of Craig's Theorem

Craig's theorem on the independence of quadratic forms in normal variates is traced from its first form, for iid standard normal variates, to the form for variates following an arbitrary nonsingular joint normal distribution. This article gives the main thrust of the development and makes recommendations on coverage of the theorem in courses and textbooks. The history of Craig's theorem is not a happy one. The authors of the earlier articles in the literature tended to make errors of a linear-algebraic nature. Authors of more recently published textbooks have given incorrect or misleadingly incomplete coverage of Craig's theorem and its proof.