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:[1]
- 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:
![{\displaystyle {\begin{bmatrix}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\end{bmatrix)).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69e612ec1fc03ec82e78e6916e75eff0bd969d42)