https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Univalent_function 2026-05-05T07:01:47Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Univalent_function&diff=238776&oldid=prev 2014-08-11T11:23:14Z

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195.37.61.178 https://en.formulasearchengine.com/index.php?title=Univalent_function&diff=8739&oldid=prev 2014-01-09T04:48:16Z

<p><span class="autocomment">Comparison with real functions</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 06:48, 9 January 2014</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><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: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Marvella </del>is <del style="font-weight: bold; text-decoration: none;">what you can contact her but it</del>'<del style="font-weight: bold; text-decoration: none;">s not </del>the <del style="font-weight: bold; text-decoration: none;">most feminine name out there</del>. <del style="font-weight: bold; text-decoration: none;">California </del>is <del style="font-weight: bold; text-decoration: none;">our birth location. For years he's been working </del>as a <del style="font-weight: bold; text-decoration: none;">receptionist. The preferred pastime for my children </del>and <del style="font-weight: bold; text-decoration: none;">me </del>is to <del style="font-weight: bold; text-decoration: none;">perform baseball but I haven't made a dime with it.</del>&lt;<del style="font-weight: bold; text-decoration: none;">br</del>&gt;&lt;<del style="font-weight: bold; text-decoration: none;">br</del>&gt;<del style="font-weight: bold; text-decoration: none;">Feel free </del>to <del style="font-weight: bold; text-decoration: none;">surf to my blog ..</del>. [<del style="font-weight: bold; text-decoration: none;">http</del>:<del style="font-weight: bold; text-decoration: none;">//Dburl.co/dietmealsdelivered20142 meal delivery service</del>]</div></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;">In [[linear algebra]], '''similarity invariance''' is a property exhibited by a function whose value is unchanged under similarities of its domain.  That is, &lt;math&gt; f &lt;/math&gt; is invariant under similarities if &lt;math&gt;f(A) = f(B^{-1}AB) &lt;/math&gt; where &lt;math&gt; B^{-1}AB &lt;/math&gt; </ins>is <ins style="font-weight: bold; text-decoration: none;">a matrix [[similar (linear algebra)|similar]] to ''A'</ins>'<ins style="font-weight: bold; text-decoration: none;">.  Examples of such functions include </ins>the <ins style="font-weight: bold; text-decoration: none;">[[trace (matrix)|trace]], [[determinant]], and the [[Minimal_polynomial_(linear_algebra)|minimal polynomial]]</ins>.</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> </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;">A more colloquial phrase that means the same thing as similarity invariance </ins>is <ins style="font-weight: bold; text-decoration: none;">"basis independence", since a matrix can be regarded </ins>as a <ins style="font-weight: bold; text-decoration: none;">linear operator, written in a certain basis, </ins>and <ins style="font-weight: bold; text-decoration: none;">the same operator in a new base </ins>is <ins style="font-weight: bold; text-decoration: none;">related </ins>to <ins style="font-weight: bold; text-decoration: none;">one in the old base by the conjugation &lt;math&gt; B^{-1}AB &lt;/math&gt;, where </ins>&lt;<ins style="font-weight: bold; text-decoration: none;">math</ins>&gt; <ins style="font-weight: bold; text-decoration: none;">B </ins>&lt;<ins style="font-weight: bold; text-decoration: none;">/math</ins>&gt; <ins style="font-weight: bold; text-decoration: none;">is the [[transformation matrix]] </ins>to <ins style="font-weight: bold; text-decoration: none;">the new base</ins>.</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> </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;">== See also ==</ins></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;">* [[Invariant (mathematics)]]</ins></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;">* [[Gauge invariance]]</ins></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;">* [[Trace diagram]]</ins></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> </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>[<ins style="font-weight: bold; text-decoration: none;">Category</ins>:<ins style="font-weight: bold; text-decoration: none;">Functions and mappings]</ins>]</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> </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> </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;">{{mathanalysis-stub}}</ins></div></td></tr> </table>

99.99.156.170 https://en.formulasearchengine.com/index.php?title=Univalent_function&diff=238775&oldid=prev 2012-05-02T21:09:13Z

<p>r2.7.1) (Robot: Adding <a href="/index.php?title=Zh:%E5%8D%95%E5%8F%B6%E5%87%BD%E6%95%B0&amp;action=edit&amp;redlink=1" class="new" title="Zh:单叶函数 (page does not exist)">zh:单叶函数</a></p> <p><b>New page</b></p><div>Marvella is what you can contact her but it&#039;s not the most feminine name out there. California is our birth location. For years he&#039;s been working as a receptionist. The preferred pastime for my children and me is to perform baseball but I haven&#039;t made a dime with it.&lt;br&gt;&lt;br&gt;Feel free to surf to my blog ... [http://Dburl.co/dietmealsdelivered20142 meal delivery service]</div>

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