magic

Magic square — square matrix where every row, column, and diagonal sums to the same value.

Syntax

M = magic(n)

Description

Returns an n×n matrix of the integers 1:n^2 arranged so that every row, every column, and both main diagonals share the same sum. n must be a positive integer. Often used as test data because the structure is unambiguous.

Examples

magic(3)                 % [8 1 6; 3 5 7; 4 9 2]
sum(magic(5))            % uniform column sums
sum(magic(5), 2)         % uniform row sums

See also

• pascal — Pascal matrix — symmetric matrix of binomial coefficients.
• eye — Identity matrix.
• zeros — Array of all zeros.