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Reference.org
Perfect matrix
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a perfect matrix is an <i>m</i>-by-<i>n</i> <a href="/facts/Binary_matrix/pS4BnBzj">binary matrix</a> that has no possible <i>k</i>-by-<i>k</i> <a href="/facts/Submatrix/qa8FI4ko">submatrix</a> K that satisfies the following conditions: </p> <ul><li><i>k</i> > 3</li> <li>the row and column sums of K are each equal to <i>b</i>, where <i>b</i> ≥ 2</li> <li>there exists no row of the (<i>m</i> − <i>k</i>)-by-<i>k</i> submatrix formed by the rows not included in K with a row sum greater than <i>b</i>.</li></ul> <p>The following is an example of a K submatrix where <i>k</i> = 5 and <i>b</i> = 2: </p> [ 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 ] . {\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}}.}