Periodic matrices of rank at least n/2 over prime-char, Q, or alg-closed char-0 fields decompose as square-zero plus torsion; always as idempotent plus torsion over any field.
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Decompositions of Periodic Matrices into a Sum of Special Matrices
Periodic matrices of rank at least n/2 over prime-char, Q, or alg-closed char-0 fields decompose as square-zero plus torsion; always as idempotent plus torsion over any field.