Generalized Tenney norms and Tp interval space: Difference between revisions
Wikispaces>mbattaglia1 **Imported revision 356543538 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 356543788 - 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 13: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-08-06 13:03:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>356543788</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]] | ||
which finally resolves to | |||
[[math]] | [[math]] | ||
\left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.\frac{9}{7}.\frac{5}{3}} = \left \| |0 \; | \left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.\frac{9}{7}.\frac{5}{3}} = \left \| |0 \;-7.925 \;\; 2.322 \;\; 5.615 \rangle \right \|_\mathbf{1} = 15.861 | ||
[[math]] | [[math]] | ||
Note that the value 15.861 is obtained by |0| + |-7.925| + |2.322| + |5.615|, which is the L1 norm of the vector. | |||
To confirm this, we can put smonzo |0 -2 1> 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> 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> | ||
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\right \|_\mathbf{1}</script><!-- ws:end:WikiTextMathRule:7 --><br /> | \right \|_\mathbf{1}</script><!-- ws:end:WikiTextMathRule:7 --><br /> | ||
<br /> | <br /> | ||
which finally resolves to<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextMathRule:8: | <!-- ws:start:WikiTextMathRule:8: | ||
[[math]]&lt;br/&gt; | [[math]]&lt;br/&gt; | ||
\left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.\frac{9}{7}.\frac{5}{3}} = \left \| |0 \; | \left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.\frac{9}{7}.\frac{5}{3}} = \left \| |0 \;-7.925 \;\; 2.322 \;\; 5.615 \rangle \right \|_\mathbf{1} = 15.861&lt;br/&gt;[[math]] | ||
--><script type="math/tex">\left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.\frac{9}{7}.\frac{5}{3}} = \left \| |0 \; | --><script type="math/tex">\left \| \vec{v} \right \|_\mathbf{T1}^\mathbf{2.\frac{9}{7}.\frac{5}{3}} = \left \| |0 \;-7.925 \;\; 2.322 \;\; 5.615 \rangle \right \|_\mathbf{1} = 15.861</script><!-- ws:end:WikiTextMathRule:8 --><br /> | ||
<br /> | |||
Note that the value 15.861 is obtained by |0| + |-7.925| + |2.322| + |5.615|, which is the L1 norm of the vector.<br /> | |||
<br /> | <br /> | ||
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.</body></html></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.</body></html></pre></div> | ||