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--- lecture_7_slides [2016/02/11 11:23] – rupert
+++ lecture_7_slides [2017/02/13 19:32] (current) – rupert
@@ Line 1: / Line 1: @@
 ~~REVEAL~~
+====== Chapter 2: The algebra of matrices ======
+==== ====
+{{page>matrix}}
+{{page>(i,j) entry}}
+==== Examples ====
+  * $B=\begin{bmatrix} 99&3&5\\7&-20&14\end{bmatrix}$ is a $2\times 3$ matrix
+    * the $(1,1)$ entry of $B$ is $b_{11}=99$
+    * the $(1,3)$ entry of $B$ is $b_{13}=5$
+    * the $(2,1)$ entry of $B$ is $b_{21}=7$
+    * etc.
+  * $(3,2)$ entry of $B$?
+    * undefined!
 ==== Examples =====
   * $\left[\begin{smallmatrix}3\\2\\4\\0\\-1\end{smallmatrix}\right]$ is a $5\times 1$ matrix.
-    * A matrix like this with one column is called a **column vector**.
+    * A **column vector**: matrix with just one column.
   * $\begin{bmatrix}3&2&4&0&-1\end{bmatrix}$ is a $1\times 5$ matrix.
-    * A matrix like this with one row is called a **row vector**.
+    * A **row vector**: matrix with just one row.
-  * Even though these have the same entries, they have a different "shape", or "size" and they are different matrices.
+  * These have the same entries, but a different "shape", or "size".
+  * They are different matrices (not equal).
 ==== Size of a matrix ====