[ 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 n-dimensional 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 .
[ adjective ] indicating the absence of any or all units under consideration
"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's-eye from 0 to 5 times .
0 time ?
Each binomial trial of a binomial experiment produces either 0 or 1 success .