# The Magic Matrix

Do you believe in the magic of numbers? If not, check out these magic matrices in this post.

The Magic Matrix

The magic matrix is a n-by-n square matrix in which every row, column and diagonal add up to the same number. Note that n is at least 3 as there are no 2 by 2 magic matrices.

Here are a few examples of magic matrices.

An example of a 3 by 3 magic matrix would be

The rows each add up 15, the columns each add up to 15 and the main diagonals add up to 15 (2 + 5 + 8 = 15 and 4 + 5 + 5 = 15).

An example of a 4 by 4 magic matrix would be

The row sums, column sums and the main diagonal sums (top left to bottom right and bottom left to top right) equal to 34.

Magic Matrices in MATLAB and R

For MATLAB, and R users creating magic matrices is quite easy.

In MATLAB, the command is magic(n) where .

In the statistical program R, the magic package needs to be installed first. After installation, the magic library needs to be summoned (bad pun). The command in R would be like in MATLAB which is magic(n).

Here is an example in R of a 11 by 11 magic matrix.

The sums of each row is 671, the sums of each column is 671 and trace of the matrix is 671.

The featured image is from http://mathworld.wolfram.com/images/eps-gif/MagicSquare_800.gif.