Permanent

The permanent of an n×n matrix $\left(\vphantom{ a_{ij}}\right.$aij$\left.\vphantom{ a_{ij}}\right)$ is the sum of certain products of the entries. Specifically,

permanent(aij) = $\displaystyle \sum_{{\sigma }}^{}$a1σ$\scriptstyle \left(\vphantom{ 1}\right.$1$\scriptstyle \left.\vphantom{ 1}\right)$a2σ$\scriptstyle \left(\vphantom{ 2}\right.$2$\scriptstyle \left.\vphantom{ 2}\right)$ ... anσ$\scriptstyle \left(\vphantom{ n}\right.$n$\scriptstyle \left.\vphantom{ n}\right)$

where σ ranges over all the permutations of $\left\{\vphantom{ 1,2,\ldots
,n}\right.$1, 2,…, n$\left.\vphantom{ 1,2,\ldots
,n}\right\}$. This operation applies to square matrices only.

$\blacktriangleright$ To compute the permanent of a matrix

1.
Place the insertion point in the matrix.

2.
From the Matrices submenu, choose Permanent.

$\blacktriangleright$ Matrices + Permanent

$\left[\vphantom{
\begin{array}{cc}
a & b \\
c & d
\end{array}
}\right.$$\begin{array}{cc}
a & b \\
c & d
\end{array}$$\left.\vphantom{
\begin{array}{cc}
a & b \\
c & d
\end{array}
}\right]$, permanent: ad + bc

$\left[\vphantom{
\begin{array}{ccc}
a_{1,1} & a_{1,2} & a_{1,3} \\
a_{2,1} & a_{2,2} & a_{2,3} \\
a_{3,1} & a_{3,2} & a_{3,3}
\end{array}
}\right.$$\begin{array}{ccc}
a_{1,1} & a_{1,2} & a_{1,3} \\
a_{2,1} & a_{2,2} & a_{2,3} \\
a_{3,1} & a_{3,2} & a_{3,3}
\end{array}$$\left.\vphantom{
\begin{array}{ccc}
a_{1,1} & a_{1,2} & a_{1,3} \\
a_{2,1} & a_{2,2} & a_{2,3} \\
a_{3,1} & a_{3,2} & a_{3,3}
\end{array}
}\right]$, permanent:
a1, 1a2, 2a3, 3 + a1, 1a2, 3a3, 2 + a2, 1a1, 2a3, 3
     + a2, 1a1, 3a3, 2 + a3, 1a1, 2a2, 3 + a3, 1a1, 3a2, 2