[seqfan] Re: [math-fun] EXACT matrix factorizations
Neil Sloane
njasloane at gmail.com
Tue May 7 22:21:10 CEST 2013
Sorry, Edwin did do the GF(2) version, which is now A225371 (and could
use more terms).
The real-valued (0,1} version - where it is a set not a ring - may or
may not be in the OEIS.
On Tue, May 7, 2013 at 2:37 PM, Neil Sloane <njasloane at gmail.com> wrote:
> Edwin, Thanks, I will enter that sequence this afternoon.
>
> I was wrong of course in calling it a ring (the result of too many
> years working in the "mod 2" world - and there the same sequence is
> also of interest but is probably in the OEIS already:
> number of nxn matrices over GF(2) that are squares). It is just a set.
>
> On Tue, May 7, 2013 at 2:17 PM, W. Edwin Clark <wclark at mail.usf.edu> wrote:
>> Brute force gives the following for a(n) = number of squares in M(n,2) =
>> ring of nxn matrices over GF(2),
>> beginning with n = 1:
>> 2,10,260,31096
>> which is not in the OEIS. Perhaps some interested soul can extend this.
>>
>> On Tue, May 7, 2013 at 1:08 PM, Neil Sloane <njasloane at gmail.com> wrote:
>>
>>> That's related to several questions that have interested me for decades.
>>> Here's a simple version: choose your favorite matrix ring R,
>>> e.g. real matrices with entries that are 0 or 1.
>>> What is a(n) := number of nxn matrices in R that have a square root in R?
>>>
>>
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>>
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>
>
>
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
--
Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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