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Let $G$ be an (additive) abelian group. Is there a concise, standard term for the order of the kernel $K$ of the endomorphism $g\mapsto 2g$? Or alternatively, for the index of $K$?

Note that this space is not a vector space, but is a convex cone in the vector space of nxn matrices (it is closed under addition and multiplication by positive scalars). Hence people sometimes refer …

Given a linear map $T:H\to H$ on an inner-product space $H$ and a subspace $K\subseteq H$, define the map $T_K = \pi_K T \pi_K^* :K \to K$, where $\pi_K:H\to K$ is the orthogonal projection. As an im …

Q1: Most often it is the maximal volume ellipsoid contained in $K$. Q2: (a) John's theorem implies that $E^+ \subseteq d E^-$ in general, and $E^+ \subseteq \sqrt{d} E^-$ if $K$ is centrally symmetri …