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Generalized Tenney norms and Tp interval space: Difference between revisions

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**Imported revision 356539642 - Original comment: **
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**Imported revision 356539736 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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>
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-08-06 12:31:13 UTC</tt>.<br>
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-08-06 12:32:03 UTC</tt>.<br>
: The original revision id was <tt>356539642</tt>.<br>
: The original revision id was <tt>356539736</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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[[math]]
[[math]]


Given these matrices, the T1 norm of our smonzo |0 1 -2&gt;, which we will call **v**, can be found by taking the L1 norm of the resulting real vector **W&lt;span style="font-size: 10px; vertical-align: sub;"&gt;L&lt;/span&gt;** · **V&lt;span style="font-size: 10px; vertical-align: sub;"&gt;G&lt;/span&gt;** · **v**. This real vector works out to |0 -7.925 2.322 5.615&gt;, and its L1 norm is |0| + |-7.925| + |2.322| + |5.615| = 15.861. This is the T1 norm of |0 1 -2&gt; on the 2.5/3.9/7 group.
Given these matrices, the T1 norm of our smonzo |0 -2 1&gt;, which we will call **v**, can be found by taking the L1 norm of the resulting real vector **W&lt;span style="font-size: 10px; vertical-align: sub;"&gt;L&lt;/span&gt;** · **V&lt;span style="font-size: 10px; vertical-align: sub;"&gt;G&lt;/span&gt;** · **v**. This real vector works out to |0 -7.925 2.322 5.615&gt;, and its L1 norm is |0| + |-7.925| + |2.322| + |5.615| = 15.861. This is the T1 norm of |0 -2 1&gt; on the 2.5/3.9/7 group.


To confirm this, we can put smonzo |0 1 -2&gt; back into rational form to see that it represents the interval 245/243. As the L1 norm is supposed to give log(n·d) for any interval n/d, we can confirm that we have the right answer above by noting that log(245·243) is indeed equal to 15.861.</pre></div>
To confirm this, we can put smonzo |0 -2 1&gt; back into rational form to see that it represents the interval 245/243. As the L1 norm is supposed to give log(n·d) for any interval n/d, we can confirm that we have the right answer above by noting that log(245·243) is indeed equal to 15.861.</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Generalized Tenney Norms and Tp Interval Space&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt; &lt;/h1&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Generalized Tenney Norms and Tp Interval Space&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt; &lt;/h1&gt;
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\end{bmatrix}&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:6 --&gt;&lt;br /&gt;
\end{bmatrix}&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:6 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Given these matrices, the T1 norm of our smonzo |0 1 -2&amp;gt;, which we will call &lt;strong&gt;v&lt;/strong&gt;, can be found by taking the L1 norm of the resulting real vector &lt;strong&gt;W&lt;span style="font-size: 10px; vertical-align: sub;"&gt;L&lt;/span&gt;&lt;/strong&gt; · &lt;strong&gt;V&lt;span style="font-size: 10px; vertical-align: sub;"&gt;G&lt;/span&gt;&lt;/strong&gt; · &lt;strong&gt;v&lt;/strong&gt;. This real vector works out to |0 -7.925 2.322 5.615&amp;gt;, and its L1 norm is |0| + |-7.925| + |2.322| + |5.615| = 15.861. This is the T1 norm of |0 1 -2&amp;gt; on the 2.5/3.9/7 group.&lt;br /&gt;
Given these matrices, the T1 norm of our smonzo |0 -2 1&amp;gt;, which we will call &lt;strong&gt;v&lt;/strong&gt;, can be found by taking the L1 norm of the resulting real vector &lt;strong&gt;W&lt;span style="font-size: 10px; vertical-align: sub;"&gt;L&lt;/span&gt;&lt;/strong&gt; · &lt;strong&gt;V&lt;span style="font-size: 10px; vertical-align: sub;"&gt;G&lt;/span&gt;&lt;/strong&gt; · &lt;strong&gt;v&lt;/strong&gt;. This real vector works out to |0 -7.925 2.322 5.615&amp;gt;, and its L1 norm is |0| + |-7.925| + |2.322| + |5.615| = 15.861. This is the T1 norm of |0 -2 1&amp;gt; on the 2.5/3.9/7 group.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
To confirm this, we can put smonzo |0 1 -2&amp;gt; back into rational form to see that it represents the interval 245/243. As the L1 norm is supposed to give log(n·d) for any interval n/d, we can confirm that we have the right answer above by noting that log(245·243) is indeed equal to 15.861.&lt;/body&gt;&lt;/html&gt;</pre></div>
To confirm this, we can put smonzo |0 -2 1&amp;gt; back into rational form to see that it represents the interval 245/243. As the L1 norm is supposed to give log(n·d) for any interval n/d, we can confirm that we have the right answer above by noting that log(245·243) is indeed equal to 15.861.&lt;/body&gt;&lt;/html&gt;</pre></div>
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