Getting Started |
Concatenation
Concatenation is the process of joining small matrices to make bigger ones. In fact, you made your first matrix by concatenating its individual elements. The pair of square brackets, []
, is the concatenation operator. For an example, start with the 4-by-4 magic square, A
, and form
The result is an 8-by-8 matrix, obtained by joining the four submatrices:
B = 16 3 2 13 48 35 34 45 5 10 11 8 37 42 43 40 9 6 7 12 41 38 39 44 4 15 14 1 36 47 46 33 64 51 50 61 32 19 18 29 53 58 59 56 21 26 27 24 57 54 55 60 25 22 23 28 52 63 62 49 20 31 30 17
This matrix is halfway to being another magic square. Its elements are a rearrangement of the integers 1:64
. Its column sums are the correct value for an 8-by-8 magic square:
But its row sums, sum(B')'
, are not all the same. Further manipulation is necessary to make this a valid 8-by-8 magic square.
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