A new short solution of the known Four Subspace Problem over an arbitrary field is presented.

Let Kn(F) be the linear space of all n × n alternate matrices over a field F. An operator f : Kn(F) → Kn(F) is said to be additive if f(A + B) = f(A) + f(B) for any A, B set membership, variant Kn(F), linear if f is additive and f(aA) = af(A) for every a set membership, variant F and A set membership, variant Kn(F), and a preserver of ranks 2 and 4 on Kn(F) if rank f(X) = rank X for every X set membership, variant Kn(F) with rank X = 2 or 4. When n greater-or-equal, slanted 4, we characterize all linear (respectively, additive) preservers of ranks 2 and 4 on Kn(F) over any field (respectively, any field that is not isomorphic to a proper subfield of itself). Furthermore, it is also shown that the condition “F is not isomorphic to a proper subfield of itself” is necessary for the obtained conclusion on additive preservers of ranks 2 and 4 on Kn(F).