https://linear.subwiki.org/w/index.php?action=history&feed=atom&title=Permutation_matrix 2026-07-14T12:52:49Z Revision history for this page on the wiki MediaWiki 1.41.2 https://linear.subwiki.org/w/index.php?title=Permutation_matrix&diff=76&oldid=prev 2014-05-01T18:06:53Z

<p><span dir="auto"><span class="autocomment">Weaker properties</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:06, 1 May 2014</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26">Line 26:</td> <td colspan="2" class="diff-lineno">Line 26:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| [[Stronger than::column-stochastic matrix]] || || || || {{intermediate notions short|column-stochastic matrix|permutation matrix}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| [[Stronger than::column-stochastic matrix]] || || || || {{intermediate notions short|column-stochastic matrix|permutation matrix}}</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr> </table>

Vipul https://linear.subwiki.org/w/index.php?title=Permutation_matrix&diff=75&oldid=prev 2014-05-01T18:06:38Z

<p>Created page with &quot;{{square matrix property}} ==Definition== A <a href="/wiki/Square_matrix" title="Square matrix">square matrix</a> is termed a &#039;&#039;&#039;permutation matrix&#039;&#039;&#039; if it satisfes &#039;&#039;&#039;both&#039;&#039;&#039; these conditions: # Every row has exactly one n...&quot;</p> <p><b>New page</b></p><div>{{square matrix property}}<br /> <br /> ==Definition==<br /> <br /> A [[square matrix]] is termed a &#039;&#039;&#039;permutation matrix&#039;&#039;&#039; if it satisfes &#039;&#039;&#039;both&#039;&#039;&#039; these conditions:<br /> <br /> # Every row has exactly one nonzero entry, and the value of that entry is 1.<br /> # Every column has exactly one nonzero entry, and the value of that entry is 1.<br /> <br /> Note that assuming that the matrix is an [[invertible matrix]], the two conditions are equivalent (and moreover, all permutation matrices are invertible). Thus, a permutation matrix can be defined as an invertible matrix satisfying condition (1), or equivalently, as an invertible matrix satisfying condition (2).<br /> <br /> ==Relation with other properties==<br /> <br /> ===Weaker properties===<br /> <br /> {| class=&quot;sortable&quot; border=&quot;1&quot;<br /> ! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions<br /> |-<br /> | [[Stronger than::monomial matrix]] || || || || {{intermediate notions short|monomial matrix|permutation matrix}}<br /> |-<br /> | [[Stronger than::signed permutation matrix]] || || || || {{intermediate notions short|signed permutation matrix|permutation matrix}}<br /> |-<br /> | [[Stronger than::doubly stochastic matrix]] || || || || {{intermediate notions short|doubly stochastic matrix|permutation matrix}}<br /> |-<br /> | [[Stronger than::row-stochastic matrix]] || || || || {{intermediate notions short|row-stochastic matrix|permutation matrix}}<br /> |-<br /> | [[Stronger than::column-stochastic matrix]] || || || || {{intermediate notions short|column-stochastic matrix|permutation matrix}}</div>

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