A bounded linear operator is a specific type of function that maps elements from one vector space to another while preserving the operations of vector addition and scalar multiplication. This means that if you take two vectors and add them, applying the operator will yield the same result as applying the operator to each vector individually and then adding the results. Additionally, a bounded linear operator has a crucial property: it does not stretch vectors too much. More formally, there exists a constant such that the operator's output is always within that constant multiplied by the input's size. This concept is essential in functional analysis and is often studied in relation to Hilbert spaces and Banach spaces.