6. Matrix Means
Friedrich Pukelsheim · Society for Industrial and Applied Mathematics eBooks · 2006
The classical criteria are introduced: the determinant criterion, the average-variance criterion, the smallest-eigenvalue criterion, and the trace criterion. They are just four particular cases of the matrix means ϕp , with parameter p ∈ [−∞; 1]. The matrix mean of a given matrix is the same as the vector mean of the eigenvalue vector of the matrix. This and a majorization inequality show the matrix mean ϕp to be an information function. Its polar is proportional to the matrix mean ϕq where the numbers p and q are conjugate in the interval [−∞; 1].