Update documentation

_sources/chapters/Week7/eofs.ipynb

@@ -60,21 +60,21 @@
     "In order to satisfy matrix multiplication rules, this can be re-written as:\n",
     "\n",
     "$$\n",
-    "\\frac{1}{M-1} \\mathbf{e_1^TX^TXe_1}\n",
+    "\\frac{1}{M-1} \\mathbf{e_1^T X^T Xe_1}\n",
     "$$\n",
     "\n",
     "This is equivalent to maximizing,\n",
     "\n",
     "$$\n",
-    "\\mathbf{e_1^TCe_1}\n",
+    "\\mathbf{e_1^T Ce_1}\n",
     "$$\n",
     "\n",
     "subject to the constraint that $\\mathbf{e_1}$ is a unit vector.\n",
     "\n",
     "If we assume the maximum value of this squared resemblance is $\\lambda_1$,\n",
     "\n",
     "$$\n",
-    "\\mathbf{e_1^TCe_1} = \\lambda_1\n",
+    "\\mathbf{e_1^T Ce_1} = \\lambda_1\n",
     "$$\n",
     "\n",
     "we find that the above equation has the same form as the eigenvalue problem we discussed in the previous section. That is, this equation becomes,\n",
@@ -139,6 +139,13 @@
     "In the next section, we will take a look at an example and go through the above procedure step-by-step."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -149,7 +156,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -163,7 +170,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.3"
+   "version": "3.10.8"
   }
  },
  "nbformat": 4,

chapters/Week7/eofs.html

@@ -171,6 +171,7 @@
 <li class="toctree-l1 has-children"><a class="reference internal" href="../Week2/hypothesis_testing.html">Statistical Hypothesis Testing</a><input class="toctree-checkbox" id="toctree-checkbox-4" name="toctree-checkbox-4" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-4"><i class="fa-solid fa-chevron-down"></i></label><ul>
 <li class="toctree-l2"><a class="reference internal" href="../Week2/probability.html">Basic Probability</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../Week2/normdist.html">The Standard Normal Distribution</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../Week2/ENSO.html">What is ENSO?</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../Week2/zstat.html">The <em>z</em>-Statistic</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../Week2/signal2noise.html">Signal-to-Noise</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../Week2/central_limit_theorem.html">The Central Limit Theorem</a></li>
@@ -475,18 +476,18 @@ <h2>Maximizing the resemblance of <span class="math notranslate nohighlight">\(\
 <p>In order to satisfy matrix multiplication rules, this can be re-written as:</p>
 <div class="math notranslate nohighlight">
 \[
-\frac{1}{M-1} \mathbf{e_1^TX^TXe_1}
+\frac{1}{M-1} \mathbf{e_1^T X^T Xe_1}
 \]</div>
 <p>This is equivalent to maximizing,</p>
 <div class="math notranslate nohighlight">
 \[
-\mathbf{e_1^TCe_1}
+\mathbf{e_1^T Ce_1}
 \]</div>
 <p>subject to the constraint that <span class="math notranslate nohighlight">\(\mathbf{e_1}\)</span> is a unit vector.</p>
 <p>If we assume the maximum value of this squared resemblance is <span class="math notranslate nohighlight">\(\lambda_1\)</span>,</p>
 <div class="math notranslate nohighlight">
 \[
-\mathbf{e_1^TCe_1} = \lambda_1
+\mathbf{e_1^T Ce_1} = \lambda_1
 \]</div>
 <p>we find that the above equation has the same form as the eigenvalue problem we discussed in the previous section. That is, this equation becomes,</p>
 <div class="math notranslate nohighlight">