The original question about eigenvectors was prompted by the
following. Eigenvectors over RDF and CDF are computed by SciPy and
returned with their eigenvalues as if each eigenvalue has algebraic
and geometric multiplicity 1. Decisions about "equal" eigenvalues are
left to the caller. SciPy norm
On Tue, Apr 20, 2010 at 9:34 AM, Jason Grout
wrote:
>
> Do you mind posting this example? Was it truly a bug (i.e., unintentional
> wrong behavior), or a result of double precision computation rounding things
> off? In other words, were the returned evals almost real? What was the
> condition n
On Tue, Apr 20, 2010 at 4:52 AM, Tim Lahey wrote:
> On Tue, Apr 20, 2010 at 7:42 AM, John Cremona wrote:
>> In summary: what is a sensible or desirable normalisation depends a
>> lot on what the field is and what sort of mathematics you are doing!
>>
>> John
>
> Matlab has a bug in its eigen rout
On 04/20/2010 06:52 AM, Tim Lahey wrote:
On Tue, Apr 20, 2010 at 7:42 AM, John Cremona wrote:
In summary: what is a sensible or desirable normalisation depends a
lot on what the field is and what sort of mathematics you are doing!
John
Matlab has a bug in its eigen routines, at least in its
John,
certainly, over exact field you don't want to create unnecessary
square roots.
(actually, I would argue against normalisation in fields like QQbar,
as division is expensive there...)
Dima
On Apr 20, 7:42 pm, John Cremona wrote:
> I would say: over an inexact field like R or C then it is se
On Tue, Apr 20, 2010 at 7:42 AM, John Cremona wrote:
> In summary: what is a sensible or desirable normalisation depends a
> lot on what the field is and what sort of mathematics you are doing!
>
> John
Matlab has a bug in its eigen routines, at least in its eigenvalue
routines so I'm
assuming th
I would say: over an inexact field like R or C then it is sensible to
normalize as Dima suggests (norm 1) rather than making any one
nonzero coordinate 1. But over exact fields (e.g. finite fields,
number fields) it does make perfect sense to normalise to the first
(or last?) nonzero coordinate
Dan,
indeed, it's not too bad to normalize to norm 1, say, but it is quite
bad to normalize a given coordinate to 1.
I cc this to sage-devel
Best,
Dima
On Apr 18, 11:21 am, Dan Drake wrote:
> On Sat, 17 Apr 2010 at 07:50PM -0700, Dima Pasechnik wrote:
> > On Apr 18, 3:29 am, William Stein wrot
