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Definition: An nXn matrix M is called a magic square if the sum of the entries is the same in each row, each column, and both diagonals. This common sum is called the weight of M, denoted wt(M). If M is an nXn magic square that contains each of the entries 1, 2,..., n^2 exactly once, then M is called a classical magic square.
Source: Linear Algebra: A Modern Introduction, 3rd edition by David Poole (note-custom edition titled Matrix Algebra)