noun
1. : a branch of mathematics that is concerned with mathematical structures closed under the operation of addition and scalar multiplication and with their applications and that includes the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations
2. : a mathematical ring which is also a vector space with scalars from an associated field and whose multiplicative operation is such that (aA)(bB)=(ab)(AB) where a and b are scalars and A and B are vectors — called also algebra