Mike's lecture on vector spaces and dual spaces: Difference between revisions
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
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<span style="font-size: 90%;">[[#ref3]][3] - This is one of those things that seems totally useless unless you're [[Gene Ward Smith|Gene Smith]], at which point you realize that multivals represent higher-rank temperaments, and that this random field of mathematics has a rather musical interpretation.</span> | <span style="font-size: 90%;">[[#ref3]][3] - This is one of those things that seems totally useless unless you're [[Gene Ward Smith|Gene Smith]], at which point you realize that multivals represent higher-rank temperaments, and that this random field of mathematics has a rather musical interpretation.</span> | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mike's Lecture on Vector Spaces and Dual Spaces</title></head><body><!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc0"><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/ | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Mike's Lecture on Vector Spaces and Dual Spaces</title></head><body><!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc0"><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/15550118?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;15550118&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"> | ||
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<!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#toc0"></a></div> | <!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#toc0"></a></div> | ||
<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#LECTURE 1: Vector Spaces and Dual Spaces">LECTURE 1: Vector Spaces and Dual Spaces</a></div> | <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#LECTURE 1: Vector Spaces and Dual Spaces">LECTURE 1: Vector Spaces and Dual Spaces</a></div> | ||
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<span style="font-size: 90%;"><!-- ws:start:WikiTextAnchorRule:23:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@ref3&quot; title=&quot;Anchor: ref3&quot;/&gt; --><a name="ref3"></a><!-- ws:end:WikiTextAnchorRule:23 -->[3] - This is one of those things that seems totally useless unless you're <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Smith</a>, at which point you realize that multivals represent higher-rank temperaments, and that this random field of mathematics has a rather musical interpretation.</span><br /> | <span style="font-size: 90%;"><!-- ws:start:WikiTextAnchorRule:23:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@ref3&quot; title=&quot;Anchor: ref3&quot;/&gt; --><a name="ref3"></a><!-- ws:end:WikiTextAnchorRule:23 -->[3] - This is one of those things that seems totally useless unless you're <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Smith</a>, at which point you realize that multivals represent higher-rank temperaments, and that this random field of mathematics has a rather musical interpretation.</span><br /> | ||
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