update build and types

pages/CSE559A/CSE559A_L22.md

@@ -166,11 +166,11 @@ y \\
 \end{pmatrix}
 $$
 
-Constraint from a match $(x_i,x_i^′)$: $x_i^′≅Hx_i$
+Constraint from a match $(x_i,x_i^')$: $x_i^'≅Hx_i$
 
 How can we get rid of the scale ambiguity? 
 
-Cross product trick:	$x_i^′ × Hx_i=0$
+Cross product trick:	$x_i^' × Hx_i=0$
 
 The cross product is defined as:
 
@@ -181,9 +181,9 @@ $$
 Let $h_1^T, h_2^T, h_3^T$ be the rows of $H$. Then
 
 $$
-x_i^′ × Hx_i=\begin{pmatrix}
-    x_i^′ \\
-    y_i^′ \\
+x_i^' × Hx_i=\begin{pmatrix}
+    x_i^' \\
+    y_i^' \\
     1
 \end{pmatrix} \times \begin{pmatrix}
     h_1^T x_i \\
@@ -192,18 +192,18 @@ x_i^′ × Hx_i=\begin{pmatrix}
 \end{pmatrix}
 =
 \begin{pmatrix}
-    y_i^′ h_3^T x_i−h_2^T x_i \\
-    h_1^T x_i−x_i^′ h_3^T x_i \\
-    x_i^′ h_2^T x_i−y_i^′ h_1^T x_i
+    y_i^' h_3^T x_i−h_2^T x_i \\
+    h_1^T x_i−x_i^' h_3^T x_i \\
+    x_i^' h_2^T x_i−y_i^' h_1^T x_i
 \end{pmatrix}
 $$
 
-Constraint from a match $(x_i,x_i^′)$:
+Constraint from a match $(x_i,x_i^')$:
 
 $$
-x_i^′ × Hx_i=\begin{pmatrix}
-    x_i^′ \\
-    y_i^′ \\
+x_i^' × Hx_i=\begin{pmatrix}
+    x_i^' \\
+    y_i^' \\
     1
 \end{pmatrix} \times \begin{pmatrix}
     h_1^T x_i \\
@@ -212,9 +212,9 @@ x_i^′ × Hx_i=\begin{pmatrix}
 \end{pmatrix}
 =
 \begin{pmatrix}
-    y_i^′ h_3^T x_i−h_2^T x_i \\
-    h_1^T x_i−x_i^′ h_3^T x_i \\
-    x_i^′ h_2^T x_i−y_i^′ h_1^T x_i
+    y_i^' h_3^T x_i−h_2^T x_i \\
+    h_1^T x_i−x_i^' h_3^T x_i \\
+    x_i^' h_2^T x_i−y_i^' h_1^T x_i
 \end{pmatrix}
 $$
 
@@ -222,9 +222,9 @@ Rearranging the terms:
 
 $$
 \begin{bmatrix}
-    0^T &-x_i^T &y_i^′ x_i^T \\
-    x_i^T &0^T &-x_i^′ x_i^T \\
-    y_i^′ x_i^T &x_i^′ x_i^T &0^T
+    0^T &-x_i^T &y_i^' x_i^T \\
+    x_i^T &0^T &-x_i^' x_i^T \\
+    y_i^' x_i^T &x_i^' x_i^T &0^T
 \end{bmatrix}
 \begin{bmatrix}
     h_1 \\