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small latex typo in ex36

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Morten Hjorth-Jensen
2023-09-04 16:27:23 +02:00
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commit 14e3712190
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doc/LectureNotes/_build/html/exercisesweek36.html
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@@ -279,6 +279,18 @@ const thebe_selector_output = ".output, .cell_output"
</a>
</li>
</ul>
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Projects
</span>
</p>
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="project1.html">
Project 1 on Machine Learning, deadline October 9 (midnight), 2023
</a>
</li>
</ul>
</div>
</nav> <!-- To handle the deprecated key -->
@@ -504,14 +516,14 @@ a finite number larger than zero. We will not implement that here.</p>
</div>
<div class="section" id="b-the-singular-value-decomposition">
<h3>b) The singular value decomposition<a class="headerlink" href="#b-the-singular-value-decomposition" title="Permalink to this headline"></a></h3>
<p>Use the singular value decomposition of an n\times p<span class="math notranslate nohighlight">\( matrix \)</span>\boldsymbol{X}$ (our design matrix)</p>
<p>Use the singular value decomposition of an <span class="math notranslate nohighlight">\(n\times p\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> (our design matrix)</p>
<div class="math notranslate nohighlight">
\[
\boldsymbol{X}=\boldsymbol{U}\boldsymbol{\Sigma}\boldsymbol{V}^T,
\]</div>
<p>where <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span> are orthogonal matrices of dimensions
<span class="math notranslate nohighlight">\(n\times n\)</span> and <span class="math notranslate nohighlight">\(p\times p\)</span>, respectively, and <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span> is an
<span class="math notranslate nohighlight">\(n\times p\)</span> matrix which contains the ingular values only. This material was discussed during the lectures of week 35.</p>
<span class="math notranslate nohighlight">\(n\times p\)</span> matrix which contains the singular values only. This material was discussed during the lectures of week 35.</p>
<p>Show that you can write the
OLS solutions in terms of the eigenvectors (the columns) of the orthogonal matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> as</p>
<div class="math notranslate nohighlight">