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Topic: Calculating matrix permanent
Replies: 9   Last Post: Feb 4, 2013 4:29 PM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Calculating matrix permanent
Posted: Feb 4, 2013 4:29 PM
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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.



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