In Barycenters in the Wasserstein space https://hal.archives-ouvertes.fr/hal-00637399/document section 6.3 The gaussian case Theorem 6.1, the authors used the order on the matrix ring by claiming the set $$ K_{\alpha,\beta}:=\{S:\alpha I\leq S\leq \beta I, S \,symmetric\} $$ is convex and compact.
I wonder what is the definition of ordering used in this case? Is it by comparing the largest eigenvalues of matrices?