Notice that if formula_5 then the weak value is equal to the usual expected value in the initial state formula_6 or the final state formula_7. In general the weak value quantity is a complex number. The weak value of the observable becomes large when the post-selected state, formula_2, approaches being orthogonal to the pre-selected state, formula_1, i.e. formula_10. If formula_11 is larger than the largest eigenvalue of formula_3 or smaller than the smallest eigenvalue of formula_3 the weak value is said to be anomalous.