An arithmetic-geometric mean inequality for singular values and its applications

In this short note, we give a new equivalent form of the arithmetic-geometric mean inequality for singular values. As applications of our result, we give a new proof of an inequality due to Bhatia and Davis (1993) [4] and we obtain a singular value inequality for matrix means, which is similar to one proved by Drury (2012) [9]. Finally, we present a log-majorization inequality for singular values.