Comments on the MAC and the NCO, and a linear modal correlation coefficient

A critical review and new insights on the modal assurance criterion (MAC) and the normalized cross orthogonality (NCO) are presented. A linear modal correlation coefficient, LNCO, is also proposed that solves the defects of previous coefficients. The disadvantage of the MAC is that it only serves as a correlation or collinearity test between eigenvectors. The NCO is a modification of the MAC customized to solve its first noted shortcoming. The LNCO is an orthogonality check does have a meaningful domain for its [0,1] rank and is linear.