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has definitions from the field of mathematics


1 
[ noun ] (mathematics) a mathematical element that when added to another number yields the same number
Used in print (Kenneth Hoffman and Ray Kunze, Linear Al...)If * * f is the operator induced on * * f by T , then evidently * * f , because by definition * * f is 0 on the subspace * * f . When * * f for each i , we shall have * * f , because the operator * * f will then be 0 on the range of * * f . Since N and N ' are both nilpotent and they commute , the operator * * f is nilpotent ; for , using the fact that N and N ' commute * * f and so when r is sufficiently large every term in this expression for * * f will be 0 . ( Actually , a nilpotent operator on an ndimensional space must have its nth power 0 ; if we take * * f above , that will be large enough . Such an operator is obviously the zero operator ; for since it is nilpotent , the minimal polynomial for this operator is of the form * * f for some * * f ; but then since the operator is diagonalizable , the minimal polynomial cannot have a repeated root ; hence * * f and the minimal polynomial is simply x , which says the operator is 0 . 
2 
[ adjective ] indicating the absence of any or all units under consideration
Synonyms Examples "a zero score" Used in print (Frederick Mosteller et al., Probability with...)A trained marksman shooting five rounds at a target , all under practically the same conditions , may hit the bull'seye from 0 to 5 times . 0 time ? Each binomial trial of a binomial experiment produces either 0 or 1 success . Related terms 
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