In this paper, we develop various calculus rules for general smooth matrix-valued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function -log X to study a new notion of...

The recent meltdown in some Asian economies highlights the urgent need of more proper measures of economic performance. Measures such as GNP growth rates alone are not good enough in revealing the true strength of an economy unless costs of capitals are also examined. In recent years, there have...