Conditions for a quadratic form to have a chi-squared distribution
Irving John Good · Biometrika · 1969
Suppose that x has a multinormal distribution and A is a symmetrio matrix. Necessary and sufficient conditions are proved for x′Ax to have a chi-squared distribution with r degrees of freedom. Let x be a column vector of n components having a multinormal distribution of mean 0 and covariance matrix C, possibly singular. Let A be an n × n symmetric matrix.