Tool to calculate the permanent of a matrix. The Permanent of a a square matrix M is a value (similar to the determinant) denoted per(M).

Permanent of a Matrix - dCode

Tag(s) : Matrix

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool to calculate the permanent of a matrix. The Permanent of a a square matrix M is a value (similar to the determinant) denoted per(M).

The permanent of a square matrix \( M = a_{i,j} \) is defined by $$ \operatorname{per}(M)=\sum_{\sigma\in S_n}\prod_{i=1}^n a_{i,\sigma(i)} $$ with \( \sigma \) the elements of the symmetric group \( S_n \).

The permanent is like the determinant of a matrix, but without the signs - (minus).

For a 2x2 matrix, the calculation of the permanent is: $$ \begin{vmatrix} a & b\\c & d \end{vmatrix}=ad + bc $$

Example: \( M = \begin{vmatrix} 1 & 2\\3 & 4 \end{vmatrix}=1 \times 4 + 2 \times 3 = 10 \)

For higher size matrix like 3x3: $$ \operatorname{per}\left( \begin{vmatrix} a & b & c\\d & e & f\\g & h & i \end{vmatrix} \right) = a \operatorname{per}\left( \begin{vmatrix} e & f\\h & i \end{vmatrix} \right) + b \operatorname{per}\left( \begin{vmatrix} d & f\\g & i \end{vmatrix} \right) + c \operatorname{per}\left(\begin{vmatrix} d & e\\g & h \end{vmatrix} \right) \\ = aei+afh+bfg+bdi+cdh+ceg $$

The idea is the same for higher order matrices.

For a 1x1 matrix, the permanent is the only item of the matrix.

As for the determinant of a matrix, the permanent of a non-square matrix is not defined.

dCode retains ownership of the source code of the script Permanent of a Matrix online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Permanent of a Matrix script for offline use on PC, iPhone or Android, ask for price quote on contact page !

permanent,matrix,per,square,determinant

Source : https://www.dcode.fr/matrix-permanent

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲