  In the present paper we introduce and investigate the notion of 2-local
linear map on vector spaces. A sufficient condition is obtained for linearity
of a 2-local linear map on finite dimensional vector spaces. Based on this
result we prove that every 2-local derivation on a finite dimensional formally
real Jordan algebra is a derivation. Also we show that every 2-local
1-automorphism (i.e. implemented by single symmetries) of mentioned Jordan
algebras is an automorphism.
