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For x,y∈â„Ân, we say x is weakly submajorized (weakly supermajorized) by y, and write x≺Éy (x≺Éy), if ∑1kx[i]≤∑1ky[i], k=1,2,…,n (∑1kx(i)≥∑1ky(i), k=1,2,…,n), where x[i] (x(i)) denotes the ith component of the vector x↓ (x↑) whose components are a decreasing (increasing) rearrangment of the components of x. We characterize the linear maps that preserve (strongly preserve) one of the majorizations ≺É or ≺É.