update equations with unique labels

notebooks/aurora/auxiliary/tf_calculation.ipynb

@@ -73,13 +73,13 @@
     "\n",
     "Extracting the first equation from the system we write:\n",
     "\n",
-    "\\begin{equation}\n",
+    "\\begin{equation*}\n",
     "\\begin{bmatrix} E_x \\end{bmatrix} \n",
     "= \n",
     "\\begin{bmatrix} Z_{xx} & Z_{xy} \\end{bmatrix} \n",
     "\\begin{bmatrix} H_x \\\\ H_y \\end{bmatrix}\n",
-    "\\label{eq:MTTF} \\tag{2a}\n",
-    "\\end{equation}\n",
+    "\\label{eq:2a} \\tag{2a}\n",
+    "\\end{equation*}\n",
     "\n",
     "\n",
     "In the \"E_x\" equation. the values for E, H are themselves vector observations\n",
@@ -97,7 +97,7 @@
     "H_{x,1} & H_{x,2} & ... & H_{x,N} \\\\\n",
     "H_{y,1} & H_{y,2} & ... & H_{y,N} \\\\\n",
     "\\end{bmatrix}\n",
-    "\\label{eq:EXTF} \\tag{2b}\n",
+    "\\label{eq:2b} \\tag{2b}\n",
     "\\end{equation*}\n",
     "$\n",
     "\n",
@@ -202,7 +202,7 @@
     "\\left<H_{x} H_{x}^* \\right> & \\left<H_{x} H_{y}^* \\right> \\\\\n",
     "\\left<H_{y} H_{x}^* \\right> &  \\left<H_{y} H_{y}^* \\right> \n",
     "\\end{bmatrix}\n",
-    "\\label{eq:EXTFHDaggerSolutionStep} \\tag{3b}\n",
+    "\\label{eq:3b} \\tag{3b}\n",
     "\\end{equation*}\n",
     "\n",
     "\n",
@@ -354,15 +354,15 @@
     "=\n",
     "\\frac{\\left< E_{x} H_{x}^{*} \\right> \\left<H_{y} H_{y}^* \\right> - \\left<E_{x} H_{y}^{*} \\right> \\left<H_{y} H_{x}^* \\right> }\n",
     "{Det(HH^{\\dagger})}\n",
-    "\\label{eq:EXTFHDaggerSolutionStepq} \\tag{6a}\n",
+    "\\label{eq:6a} \\tag{6a}\n",
     "\\end{equation*}\n",
     "\n",
     "\\begin{equation*}\n",
     "Z_{xy}\n",
     "=\n",
     "\\frac{\\left<E_{x} H_{y}^{*} \\right> \\left<H_{x} H_{x}^* \\right> - \\left< E_{x} H_{x}^{*} \\right> \\left<H_{x} H_{y}^* \\right>}\n",
     "{Det(HH^{\\dagger})}\n",
-    "\\label{eq:EXTFHDaggerSolutionStep} \\tag{6b}\n",
+    "\\label{eq:6b} \\tag{6b}\n",
     "\\end{equation*}"
    ]
   },