
Re: Calculating matrix permanent
Posted:
Feb 4, 2013 4:29 PM


On Feb 4, 9:00 am, "J.B. Wood" <john.w...@nrl.navy.mil> wrote: > On 02/01/2013 05:09 PM, Butch Malahide wrote: > > > The OED's earliest citation for the term "permanent" in this sense is > > from A. C. Aitken in 1939: > > > 1939 A. C. Aitken Determinants & Matrices ii. 30 The corresponding > > sum with terms all positive is called the permanent of A; its > > properties are neither so simple nor so rich in application as those > > of determinants, but it has an importance in the theory of symmetric > > functions and in abstract algebra. > > > So the permanent of a matrix is older than Wikipedia or the internet, > > and it *has* been around "since the time of Greek mathematicians": > > there were Greek mathematicians in 1939, as there are today. > > Hello, and I stand corrected. I also should have said "ancient" Greek > mathematicians. I'll stand by my comments on Wikipedia. I'm an EE by > profession and none of my applied math textbooks mention "permanent". > Other matrix properties/type such as determinant, inverse, diagonal, > trace, skew, hermetian, eigenvalues) are dealt with in detail, however.
Well, nobody ever claimed permanents were as important as determinants! Their applications are mainly in combinatorial mathematics, e.g., the number of perfect matchings in a bipartite graph is the permanent of the adjacency matrix. I see from the Wikipedia article that they also have some use in quantum physics. And I see that the concept of a matrix permanent is older than 1939; Van der Waerden's Permanent Conjecture (now a theorem, having been proved by Egorichev and Falikman independently around 1980), that the permanent of a doubly stochastic matrix of order n is at least n!/n^n, was formulated in 1926.

