Definitions
Let U, V be two vector spaces. The mapping from U to V is called an operator. Let V be a vector space over the field K. We can define the structure of a vector space on the set of all operators from U to V:
for all A, B: U → V, for all x in U and for all α in K.
Additionally, operators from any vector space to itself form a unital associative algebra:
with the identity mapping (usually denoted E, I or id) being the unit.
Read more about this topic: Operator (mathematics)
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