Perfect matrix
an m-by-n binary matrix that has no possible k-by-k submatrix K
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:
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:
[
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
]
.
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This entry incorporates text from “Perfect matrix” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.