Abstract
We review a general parameterization of order-3 magic squares due to Lucas and sequentially compound it to produce parameterized magic square matrices of order n=3ℓ(ℓ=2,3,…). Expressions are found for the singular values of the compound matrices. From the singular values, the Frobenius norm, and consideration of the balanced ternary numeral system, we determine numerical values for the parameters in a compound Lucas square so that it is natural (having elements 0,1,…,n2−1). A less general parameterization due to Frierson is related to Lucas' parameterization and our results specialize to it, complementing previous results.
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