Re: why does professor david c ullrich have to put people down to feel good about himself?

David C. Ullrich a écrit :
On Sun, 30 Nov 2008 22:35:28 -0800 (PST),
lwalke3@xxxxxxxxx wrote:

On Nov 30, 2:23 am, Denis Feldmann
<denis.feldmann.sanss...@xxxxxxx>
wrote:
lwal...@xxxxxxxxx a écrit :
By now, I'm starting to wonder whether there's
_anything_ that
Ullrich will accept as a 100% rigorous, 100%
valid definition
of A^C.
For instance, one could start by =reading= about
log of matrices, or
even before that, about eigenvalues...
I already know about eigenvalues. I already know
that
for a matrix A, if there exists a scalar lambda
and a
nonzero vector v such that Av = lambda v, then we
call lambda an eigenvalue (my old linear algebra
teacher abbreviated this "eit" for some strange
reason") and v an eigenvector of the matrix. And
if
there are as many linearly independent vectors as
the
dimension of the matrix, then we can diagonalize
the
matrix A = PDP^-1, where P is a matrix whose
column
vectors are eigenvectors of A and D is a diagonal
matrix with the eits of A on the diagonal.

Does tommy1729 know about eigenvalues? I don't
know,
but as mentioned in the other thread, many of the
properties of the matrix necessary for finding a
logarithm, that tommy1729 ascribes to the
determinant
of the matrix, are actually more applicable to the
eigenvalues of the matrix.

Feldmann assumed that I knew nothing about
eigenvalues
because my posts are based on tommy1729's, and he
fails to mention them.

Maybe we should even change the conjecture so that
it
refers to eigenvalues, not determinants:

For all matrices A,B with _eigenvalues_ not
0,+/-1,
AB = BA iff there exist matrices C,D such that
exp(D) = A, CD = DC, and exp(CD) = B.

As long as Robert's already given everything away,
someone should point out two things: First, the
condition about eigenvalues not equalling 1 or -1
is not needed - I've asked a few times and nobody's
explained why anyone would imagine that that
had any relevance.



Easy : the numbers 1 and -1 appears at one or two
places here (like at
bondaries for convergence of the series for ln (1+x).
For people not
knowing (and not willing to do) any math, and juist
looking (not even
very deeply) at Web references, it seems like a
reasonable condition to
add "just in case"...

Second, it's easy to see that the conjecture is
equivalent to a more symmetric version: Given
invertible matrices A and B, we have AB = BA
if and only if there exist C and D with CD = DC
and A = exp(C), B = exp(D).

(Note I didn't say that the existence of C and D as
in
your version is equivalent to the existence of C
and
D as in my version.)

Again, this is easy : your version looks correct.
Otoh, what do you do
for non invertible matrices? Got you, there...


Finally, it's curious that nobody's pointed out
that a "criterion" for establishing that two
matrices
commute that depends on two other matrices
commuting seems a little curious.

Curiouser and curiouser. But then, the usual
criterions of tommy (or si
it Timmy, or amy? we need a criterion here too : do
those aliases
commute?) are much more convoluted : remember the one
he gave for
analicity a while ago?

its was only a conjecture and it is still unresolved ...

besides my reply to david is more logical check it out.




David C. Ullrich

"Understanding Godel isn't about following his
formal proof.
That would make a mockery of everything Godel was
up to."
(John Jones, "My talk about Godel to the
post-grads."
in sci.logic.)

regards

tommy1729
.

Relevant Pages

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