linearspace
Linear space, often called a vector space, is a set V equipped with two operations: addition and scalar multiplication, where the elements of V can be added together and scaled by elements of a field F. These operations satisfy the vector space axioms: closure under addition and scalar multiplication; addition is commutative and associative with a zero vector and additive inverses; scalar multiplication distributes over vector addition and field addition, and is compatible with field multiplication, with 1 acting as the identity on V. When these conditions hold, V is a linear space over F.
Subspaces are subsets that are themselves linear spaces under the same operations; equivalently, W is a subspace
Linear maps (or operators) are functions T: V -> W that preserve addition and scalar multiplication. The
Common examples include R^n with ordinary addition and multiplication, polynomials with real coefficients, and function spaces.