Perfect matrix
Encyclopedia
In mathematics
, a perfect matrix is an m-by-n binary matrix that has no possible k-by-k submatrix K that satisfies the following conditions:
The following is an example of a K submatrix where k = 5 and b = 2:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a perfect matrix is an m-by-n binary matrix that has no possible k-by-k submatrix K that satisfies the following conditions:
- k > 3
- the row and column sums of K are each equal to b, where b ≥ 2
- there exists no row of the (m − k)-by-k submatrix formed by the rows not included in K with a row sum greater than b.
The following is an example of a K submatrix where k = 5 and b = 2:
