 The matrix "J" is sometimes referred to as the exchange matrix.An "n × n" matrix "A" is said to be "skew-centrosymmetric" if its entries satisfy "A"i,j = -"A"n−i+1,n−j+1 for 1 ≤ i,j ≤ n. Equivalently, "A" is skew-centrosymmetric if "AJ = -JA", where "J" is the exchange matrix defined above.The centrosymmetric relation "AJ = JA" lends itself to a natural generalization, where "J" is replaced with an involutory matrix "K" (i.e., "K2 = I")

 or, more generally, a matrix "K" satisfying "Km = I" for an integer "m > 1".