$\mathcal{A}$ 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}
\end{section}
\begin{section}{Common}
- The function $f$ applied to $x$ is $f\of{x}$. We can group terms
- like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c - d}}$. The tuples
- go up to seven, for now:
+ The function $f$ applied to $x$ is $f\of{x}$, and the restriction
+ of $f$ to a subset $X$ of its domain is $\restrict{f}{X}$. We can
+ group terms like $a + \qty{b - c}$ or $a + \qty{b - \sqty{c -
+ d}}$. The tuples go up to seven, for now:
%
\begin{itemize}
\begin{item}
\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
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-$n$