The American Mathematical Monthly, Volume 119, No. 1, by Scott T. Chapman (Editor)

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An element w satisfying the latter condition must be effective. In general, however, there may be quasi-effective vectors which are not effective. 2, for instance, the vector w = 27 e1 + 32 e2 + 23 e3 + 23 e4 − 12 e5 is quasieffective, since it is numerically equivalent to the effective vector 2e1 + e5 . Here is another example, which shows that the notion of quasi-effectiveness is “volatile” as one passes to subspaces. 4. Start with the following (2k) × (2k) matrix:   1 0 1 0 ··· 1 0 0 0 1 0 ··· 1 0   1 1 1 0 ··· 1 0   0 0 0 0 ··· 1 0.