sci.math Google Group

Re: defining log(A) for matrix A. with det =/= 0

2008-12-01T22:08:03Z

it is almost always an issue of miscommunication
there are "standard" communications
the ones sanctioned in the halls of academia
and handed down through texts and demonstration
and there are "other" communications
those generated from somewhere else
either personal exploration
or attempts at foreign translation

Re: MatheRealism

2008-12-01T21:57:11Z

Unless it is a name or a thing that cannot exist but as a name.
Yes, very romantic minds. But romantics is not a good ground for
raising mathematics. Alas, you prefer numbers that have no address. So
there is no point of discussing with you.
Soloman Feferman: Platonism is the medieval metaphysics of

Co-Compositeness (a game)

2008-12-01T21:55:53Z

This is a game for any number of players. Start with an n-by-n grid,
where n is larger if there are more players. (I suggest an n of at
least 16 if there are 2 players.)
The first player to move places a 1 in any of the grid's squares.
Players take turns placing numbers in the grid's squares as follows:

Re: Linear map preserving positive definite matrices

2008-12-01T21:53:37Z

On 2 nov, 07:08, Robert Israel <isr...@math.MyUniversitysInit ials.ca>
wrote:
Dear Robert,
Thanks for your answer,
I may have taken this result for granted a little bit too quickly...
Actually I've seen this result in a set of papers on Jordan Algebras
and bounded symmetric domains (from different authors),

Re: obtaining a numerical evaluation of log(2) with mathematica

2008-12-01T21:48:28Z

First - I am not sure what Ln is (unless it is new), the command is
Log - for any base - with defualt being natural log.
You could use postfix notation as in Log[2]//N
You could also use N[Log[2]].
If you want more precision, you could also use N[Ln[2],100000]
That should at least get you started with the commands - so you can

Re: consistency of arithmetic

2008-12-01T21:43:06Z

On Dec 1, 1:29 pm, Denis Feldmann <feldmann.denis.asuppri...@neu f.fr>
wrote:
Just to be clear, Godel completeness may be stated in this form: If a
set of formulas G (such as a theory) is consistent, then G has a model
M (M satisfies all the members of G).
On the other hand, the principle that "if a set of formulas G (such as

Re: defining log(A) for matrix A. with det =/= 0

2008-12-01T21:33:12Z

David R Tribble a écrit :
Perhaps a look at Wikipedia would prevent some of the name calling :-)
is it possible, then, to actually
Yes, it is
Is your left better than your right ? What if we write columns instead
of lines ? And why not use 1/2(exp(B log(A)) + exp(log(A) B))?
Why not? You are free to define anything anyway you like, as long as

Re: consistency of arithmetic

2008-12-01T21:29:39Z

A N Niel a écrit :
Actually, it mostly use a confusion between the formal notion of model
(for which the result of consistency is well-known since Godel) and the
idea of "the natural numbers", which is *not* a model, being not
formalised (and in some theories, the naïve integers are not even a

Re: bluster

2008-12-01T21:15:37Z

Then what did I write about "xex" that she takes exception to and that
she thinks is to be "not on the side of mathematical advancement"?
MoeBlee

Re: defining log(A) for matrix A. with det =/= 0

2008-12-01T21:11:28Z

Okay, so assuming there is a workable definition of log(A) somewhere
amidst all the name-calling, is it possible, then, to actually
calculate
something A^B for some simple (2x2) examples?
Was it ever made clear whether A^B = exp(B log(A)) was a better
or worse choice than exp(log(A) B)?
Should we conclude that root{B}(A) = exp(inv(B) log(A))?

Re: lets turn the tables

2008-12-01T21:10:23Z

FYI, I said: not *that* interested.
Just as serious as you -- and co. Stick together.
-LV

Re: Conjugate of homographic functions

2008-12-01T21:10:11Z

"Homographic" = "fractional linear"?
h3 must map the fixed points of h2 (on the Riemann sphere) to
fixed points of h1. In particular, h1 and h2 must have the same
number of fixed points. But that won't be enough to determine the
fractional linear transformation.
Case 1: h1 and h2 each have one fixed point. We may assume

Re: consistency of arithmetic

2008-12-01T21:09:31Z

In article
<3366ed41-1235-46c8-b0e8-0480d 736f...@j39g2000yqn.googlegrou ps.com>,
As I read it, he says: It is known that if a theory has a model, then
the theory is consistent. But in fact PA has the natural numbers as a
model, therefore PA is consistent.

Re: t.v.s

2008-12-01T21:01:58Z

In article
<15674010.1228159561342.JavaMa il.jaka...@nitrogen.mathforum. org>,
becasue it's contractible?

Re: A third matrix C ...

2008-12-01T21:01:52Z

On Dec 1, 3:33 am, "alainvergh...@gmail.com" <alainvergh...@gmail.com>
wrote:
My point was that if C is invertible,
then yes, A,B are similar matrices:
A*C = C*B implies A = C*B*C^-1
and thus A,B share a characteristic
polynomial (and the other invariants).
If C not invertible, more possibilities
exists. Indeed for C = 0 (zero matrix)