Stony Brook Algorithm Repository


Determinants and Permanents

Input
Output

Input Description: An \(n x n\) matrix \(M\).
Problem: What is the determinant \(|M|\) or the permanent \(Perm(M)\) for matrix \(m\)?

Excerpt from The Algorithm Design Manual: Determinants of matrices provide a clean and useful abstraction in linear algebra that can used to solve a variety of problems:

A closely related function, called the permanent, arises often in combinatorial problems. For example, the permanent of the adjacency matrix of a graph \(G\) counts the number of perfect matchings in \(G\).


Implementations

LINPACK (rating 10)
JScience (rating 9)
Barvinok 1 (rating 8)
Barvinok 2 (rating 8)
HODLR (rating 6)
Nijenhuis and Wilf (rating 5)


Recommended Books

Matrix Computations by Gene H. Golub and Charles F. Van Loan Numerical Recipes in Fortran 90 by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery Numerical Recipes in Fortran 77 by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery
Numerical Recipes in Pascal by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery Numerical Recipes in C by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery Data Structures and Algorithms by A. Aho and J. Hopcroft and J. Ullman
Permanents by H. Minc Combinatorial Algorithms for Computers and Calculators by A. Nijenhuis and H. Wilf A survey of modern algebra by G. Birkhoff and S. MacLane

Related Problems


Robust Geometric Primitives

Solving Linear Equations

Matching

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