2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170615We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of arbitrary extrinsic symmetric spaces in pseudo-Euclidean spaces by corresponding infinitesimal objects.22 pages, v2 with corrections to Prop. 6.2Differential Geometry53C50; 53C35; 53C40text