C. G. Khatri
and C. R. Rao
[J. Multivariate Anal. 11, 498-505 (1981; Zbl 0482.15010
)] gave a bound to the ratio of the determinants
, where X is an
matrix of rank k, and B, C are commutative matrices. In this paper, we provide bounds to the ratios of the determinants
and a more general result than that of Khatri and Rao. The results can be applied to some problems in statistics.