Add \unit{} for the multiplicative identity element.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index c7959732d44ce74297d43c228dd90ae267dd255a..65e0c80b69f960cb07f1e2790c61eb12e6b1e911 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -36,6 +36,9 @@
     $\mathcal{A}$ and if $x,y,z \in \mathcal{A}$, then
     $\alg{\set{x,y,z}}$ is the smallest subalgebra of $\mathcal{A}$
     containing the set $\set{x,y,z}$.
+
+    If $R$ has a multiplicative identity (that is, a unit) element,
+    then that element is denoted by $\unit{R}$.
   \end{section}
 
   \begin{section}{Algorithm}
@@ -98,7 +101,9 @@
       \end{item}
     \end{itemize}
     %
-    The factorial of the number $10$ is $\factorial{10}$.
+    The factorial of the number $10$ is $\factorial{10}$, and the
+    least common multiple of $4$ and $6$ is $\lcm{\set{4,6}} =
+    12$.
 
     The direct sum of $V$ and $W$ is $\directsum{V}{W}$. Or three
     things, $\directsumthree{U}{V}{W}$. How about more things? Like
@@ -170,7 +175,8 @@
     their tensor product is $\tp{x}{y}$. The Kronecker product of
     matrices $A$ and $B$ is $\kp{A}{B}$. The adjoint of the operator
     $L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is
-    $\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
+    $\transpose{L}$. Its trace is $\trace{L}$, and its spectrum---the
+    set of its eigenvalues---is $\spectrum{L}$. Another matrix-specific
     concept is the Moore-Penrose pseudoinverse of $L$, denoted by
     $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
     $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$