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Magic square
M = magic(n)
M = magic(n) returns an n-by-n matrix constructed from the integers 1 through n^2 with equal row and column sums. The order n must be a scalar greater than or equal to 3.
The magic square of order 3 is
M = magic(3) M = 8 1 6 3 5 7 4 9 2
This is called a magic square because the sum of the elements in each column is the same.
sum(M) = 15 15 15
And the sum of the elements in each row, obtained by transposing twice, is the same.
sum(M')' = 15 15 15
This is also a special magic square because the diagonal elements have the same sum.
sum(diag(M)) = 15
The value of the characteristic sum for a magic square of order n is
sum(1:n^2)/n
which, when n = 3, is 15.
If you supply n less than 3, magic returns either a nonmagic square, or else the degenerate magic squares 1 and [].