Let we have
list = {{1, 0, 2, 0, 1, 1}, {1, 1, 0, 1, 2, 1}, {1, 0, 0, 2, 1, 1},
{1, 1, 1, 2, 1, 1}, {2, 1, 1, 0, 1, 1}, {1, 2, 1, 2, 2, 1},
{2, 1, 1, 2, 1, 2}, {1, 2, 1, 1, 1, 1}, {0, 1, 1, 0, 1, 0},
{0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 0, 0, 1}};
I would like to obtain the list of all possible 6 x 6 matrices which are created considering every 6 tuples in the above list.
From this list, I would like to have a list of matrices where the absolute value of the determinant is bigger than 1. When we interchange two columns or rows in the matrix, we can have a minus version of the determinant, so we may have lots of repetitions. Moreover, there should not be repetition in the list.
Addition to above problem, let us consider the above algorithm for 15 x 15 matrices as follows:
list = {{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 1,
1, 0, 2, 1, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0,
1, 1, 0, 1}, {0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 4, 2}, {0, 1,
1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3}, {1, 1, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0}, {1, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1,
1}, {2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2}, {1, 2, 4, 1, 3,
4, 2, 1, 1, 2, 1, 1, 2, 2, 2}, {1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1,
1, 1, 1, 1}, {1, 1, 2, 4, 3, 1, 0, 9, 7, 6, 3, 4, 5, 6, 7}, {1, 2,
4, 5, 6, 1, 2, 1, 3, 6, 8, 6, 2, 8, 9}, {1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 0, 0, 0}, {0, 0, 1, 2, 1, 5, 7, 8, 5, 7, 3, 2, 4, 3,
3}, {3, 5, 8, 3, 0, 5, 3, 4, 3, 3, 4, 6, 3, 3, 3}, {3, 5, 7, 8, 3,
9, 5, 3, 6, 3, 3, 9, 6, 3, 3}, {3, 5, 7, 8, 3, 0, 5, 3, 4, 6, 9,
4, 4, 6, 3}};
s = Select[Subsets[list, {Length[list[[1]]]}], Abs@Det[#] > 1 &];
Length[s]
p = Flatten[Permutations /@ s, 1];
rowID = Flatten[Position[list, #] & /@ #] &;
Dataset[{Row[{"Det", MatrixForm[#], " = ", Det[#], ", Permutation ",
MatrixForm@rowID[#]}] & /@ s} // Transpose, MaxItems -> 1]
When I ran the above code I got length[s] = 136 and also message that
General: The current computation was aborted because there was insufficient \ memory available to complete the computation.
Throw: Uncaught SystemException returned to top level. Can be caught with Catch[[Ellipsis], _SystemException].
SystemException["MemoryAllocationFailure"]
Even I got the above errors, I got the list of 136 matrices which satisfies the condition described in the code. The list is given 20 matrices by 20 Matrices. How can I see whole list at one time? How can we adjust Dataset for this?