does this matrix represent some string [closed]

Question

One of my friends asked me this.. What does this represent? Some string?

   A B C D
 A = > < >
 B < = < <
 C > > = >
 D < > < =

the only thing I have been able to get till now is C>A>D>B

Answer 1

It represents a strict linear order on the set whose elements are A,B,C,D. A simple program can extract the order in "linear form" from such a matrix, e.g. by coding <,=,> as 1,0,-1 respectively, and A,B,C,D,... as 0,1,2,3,... respectively.

Here's the program from the link, applied to your question:

def order_from_matrix(m):
    return [(len(m) - 1 - sum(row)) // 2 for row in m] 

order_from_matrix([[ 0, -1,  1, -1],
                   [ 1,  0,  1,  1],
                   [-1, -1,  0, -1],
                   [ 1, -1,  1,  0]])

This produces the output

[2, 0, 3, 1]

which represents

C > A > D > B

NB: The given matrix is interpreted such that the symbols in the first row = > < > mean A=A, A>B, A<C, A>D, coded as [ 0, -1, 1, -1], and so on for the other rows. This is the interpretation consistent with C > A > D > B stated by the OP; however, the "opposite" interpretation is also possible, but would correspond to a different ordering.