From 321238b5424cd4df74c1643667f98de74b1fd05d Mon Sep 17 00:00:00 2001
From: Mark <mark@betalupi.com>
Date: Mon, 19 Feb 2024 13:54:53 -0800
Subject: [PATCH] Minor edits

---
 .../src/parts/01 bits.tex                     | 36 ++++---------------
 1 file changed, 6 insertions(+), 30 deletions(-)

diff --git a/Advanced/Introduction to Quantum/src/parts/01 bits.tex b/Advanced/Introduction to Quantum/src/parts/01 bits.tex
index 4c21c54..ba444dc 100644
--- a/Advanced/Introduction to Quantum/src/parts/01 bits.tex	
+++ b/Advanced/Introduction to Quantum/src/parts/01 bits.tex	
@@ -462,48 +462,24 @@ Thus,
 \end{equation*}
 
 
-\begin{ORMCbox}{Review: Matrix Multiplication}{black!10!white}{black!65!white}
-	Matrix multiplication works as follows:
-
+\begin{ORMCbox}{Review: Multiplying Vectors by Matrices}{black!10!white}{black!65!white}
 	\begin{equation*}
-		AB =
+		Av =
 		\begin{bmatrix}
 			1 & 2 \\
 			3 & 4 \\
 		\end{bmatrix}
 		\begin{bmatrix}
-			a_0 & b_0 \\
-			a_1 & b_1 \\
+			v_0 \\ v_1
 		\end{bmatrix}
 		=
 		\begin{bmatrix}
-			1a_0 + 2a_1 & 1b_0 + 2b_1 \\
-			3a_0 + 4a_1 & 3b_0 + 4b_1 \\
+			1v_0 + 2v_1 \\
+			3v_0 + 4v_1
 		\end{bmatrix}
 	\end{equation*}
 
-
-	Note that this is very similar to multiplying each column of $B$ by $A$. \par
-	The product $AB$ is simply $Ac$ for every column $c$ in $B$:
-
-	\begin{equation*}
-		Ac_0 =
-		\begin{bmatrix}
-			1 & 2 \\
-			3 & 4 \\
-		\end{bmatrix}
-		\begin{bmatrix}
-			a_0 \\ a_1
-		\end{bmatrix}
-		=
-		\begin{bmatrix}
-			1a_0 + 2a_1 \\
-			3a_0 + 4a_1
-		\end{bmatrix}
-	\end{equation*}
-
-	This is exactly the first column of the matrix product. \par
-	Also, note that each element of $Ac_0$ is the dot product of a row in $A$ and a column in $c_0$.
+	Note that each element of $Av$ is the dot product of a row in $A$ and a column in $v$.
 \end{ORMCbox}
 
 \problem{}