tex

1 files changed, 9 insertions, 9 deletions

diff --git a/ClassJune26.page b/ClassJune26.page
index eea5dff..9bb4ded 100644
--- a/ClassJune26.page
+++ b/ClassJune26.page
@@ -77,14 +77,14 @@ b\end{array}\right)\\
 0\\
 1\end{array}\right)\\
  = a\cdot1+b\cdot i\\
- = a+bi\end{eqnarray*}
+ = a+bi$
 Put another way, we are using $1$ and $i$ as basis vectors. For
-example, $
-\left(\begin{array}{c}
+example, 
+$\left(\begin{array}{c}
 3\\
 2\end{array}\right)=3(\rightarrow)+2(\uparrow)=3+2i$
-and $
-\overset{2}{\nwarrow}=\left(\begin{array}{c}
+and 
+$\overset{2}{\nwarrow}=\left(\begin{array}{c}
 -\sqrt{2}\\
 \sqrt{2}\end{array}\right)=-\sqrt{2}(\rightarrow)+\sqrt{2}(\uparrow)=-\sqrt{2}+\sqrt{2}i$
 
@@ -108,16 +108,16 @@ by some fixed complex number $\rho=r(\cos\theta+i\sin\theta)=a+bi$,
 which, as we saw before, is a dilation by $r$ plus a rotation by
 $\theta$. The distributive law says precisely that this is a linear
 transformation of the plane, viewed as a two-dimensional vector space.
-And linear maps are given in rectangular coordinates by matrices:\[
-\left(\begin{array}{c}
+And linear maps are given in rectangular coordinates by matrices:
+$\left(\begin{array}{c}
 x\\
-y\end{array}\right)\rightsquigarrow\left(\begin{array}{cc}
+y\end{array}\right)\mapsto\left(\begin{array}{cc}
 a & c\\
 b & d\end{array}\right)\left(\begin{array}{c}
 x\\
 y\end{array}\right)=\left(\begin{array}{c}
 ax+cy\\
-bx+dy\end{array}\right).\]
+bx+dy\end{array}\right).$
 What is the matrix corresponding to multiplication by $\rho$? Well,
 the first column is the image of $\left(\begin{array}{c}
 1\\