linalg(deprecated)
permanent
compute the permanent of a matrix
Calling Sequence
Parameters
Description
Examples
permanent(A)
A

square matrix
Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[Permanent], instead.
 For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
The permanent of a matrix is computed in a way similar to the determinant. The permanent of an arbitrary 2x2 matrix, $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$, is $\mathrm{ad}+\mathrm{bc}$. To compute the permanent of larger matrices, minor expansion is used in the same manner as when computing determinants, only without alternating sign while expanding along a row or column.
The command with(linalg,permanent) allows the use of the abbreviated form of this command.
$\mathrm{with}\left(\mathrm{linalg}\right)\:$
$A\u2254\mathrm{matrix}\left(\left[\left[1\,2\,3\right]\,\left[4\,5\,6\right]\,\left[7\,8\,9\right]\right]\right)$
${A}{\u2254}\left[\begin{array}{ccc}{1}& {2}& {3}\\ {4}& {5}& {6}\\ {7}& {8}& {9}\end{array}\right]$
$\mathrm{permanent}\left(A\right)$
${450}$
$B\u2254\mathrm{matrix}\left(\left[\left[a\,b\,c\right]\,\left[d\,e\,f\right]\,\left[g\,h\,i\right]\right]\right)$
${B}{\u2254}\left[\begin{array}{ccc}{a}& {b}& {c}\\ {d}& {e}& {f}\\ {g}& {h}& {i}\end{array}\right]$
$\mathrm{permanent}\left(B\right)$
${a}{}{e}{}{i}{+}{a}{}{f}{}{h}{+}{b}{}{d}{}{i}{+}{b}{}{f}{}{g}{+}{c}{}{d}{}{h}{+}{c}{}{e}{}{g}$
See Also
linalg(deprecated)[det]
LinearAlgebra
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