Sentence:  If T is a <WSD>linear</WSD> operator on an arbitrary vector space and if there is a monic polynomial p such that * * f , then parts ( a ) and ( b ) of Theorem 12 are valid for T with the proof which we gave . 
Meaning of the word marked with <WSD> tags:  an operator that obeys the distributive law: A(f+g) = Af + Ag (where f and g are functions)