HDTenEightyP/NetNews huggingface dataset:
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: HELP: INTEGRAL
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Tue, 5 Jan 1993 14:07:22 GMT

In article <4540017@hpcc01.corp.hp.com> selee@hpcc01.corp.hp.com (Lee Say Eng) writes:
:
:
:I am running an experiment to find a constant n and the situation
:is such that I need to find an expression for the following integral
:(in which n appears) first. 
:
:
:	   /
:	   |       p
:	   |   __________  dp       where k1, k2 and n are constants
:	   |            n  
:	   |   k1 - k2*p 
:	   /
:
:
:I've tried a few ways of doing it but haven't had any success. 
 

The way to do this is as follows:

Solve k2*p^n - k1 = 0.  The solutions are (k1/k2)^(1/n) times the
n'th roots of unity. This allows you to completely factor k1 - k2 * p^n
into linear factors. Now decompose it into partial fractions and integrate
term by term. A symbolic algebra package will help.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: kraai4712@iscsvax.uni.edu
Newsgroups: sci.math
Subject: Re: Rounding Rules
Date: 6 Jan 93 08:14:07 -0600
Organization: University of Northern Iowa

Good morning,

In article <1993Jan4.142226.9639@iscsvax.uni.edu>, kraai4712@iscsvax.uni.edu writes:
> My personal favorite rounding rule is to round anything that has {0,1,2,3,4} in
> the "rounding place" "down" and anything that has {5,6,7,8,9} "up".  So as in
> the previous example, 1.13500 would be rounded to 1.14 and 1.14500 would be
> rounded to 1.15.
> 
> To this my teachers always gasped that this method was biased, and no amount of
> pursuasion using the above-mentioned sets could pursuade them.

Thank you all for letting me know I was wrong and why and especially for doing
it nicely.  Have a great day!

jim
From: hougen@focus.csl.uiuc.edu (Darrell Roy Hougen)
Newsgroups: sci.math
Subject: What is the 'sinc' function?
Date: 12 Jan 1993 03:39:29 GMT
Organization: Center for Reliable and High-Performance Computing, University of Illinois at Urbana-Champaign
NNTP-Posting-Host: focus.csl.uiuc.edu
Summary: What is the 'sinc' function?
Keywords: sinc

I came accross it in a paper about the scattering of electromagnetic
radiation. 

Thanks.

Darrell R. Hougen
Newsgroups: sci.math
From: matmcinn@nuscc.nus.sg (brett mcinnes)
Subject: Re: Frankly,my dear......was: Fermat's Last Theorem
Organization: National University of Singapore
X-Newsreader: Tin 1.1 PL4
Distribution: usa
Date: Fri, 8 Jan 1993 02:35:47 GMT

asimov@wk223.nas.nasa.gov (Daniel A. Asimov) writes:
: In article <1993Jan7.021308.10566@nuscc.nus.sg> matmcinn@nuscc.nus.sg (.) writes:
: >
: >I wonder if this might not be an occasion for some soul- searching on the
: >part of professional mathematicians. X^n+ y^n = Z^n has no solutions....  
: >frankly, who cares? It's recreational mathematics, right? The only reason
: >anyone cares about it is that the proof is hard. Let me give you an
: >example to show you what I mean. Theorem: 2 and 4 are the only unequal
: >integers such that x^y = y^x. Why is this theorem not famous? Because [a]
: >it is boring and [b] the proof is easy. But I think it is no more boring
:  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
: 
: Oh, one more characteristic:  [c] it is false.  (Consider -2 and -4.)
: 
Good work. But I thought I should give my theorem a fighting chance of
being interesting by ensuring that it is false in advance. As you know,
theorems in elementary number theory are only regarded as interesting if
they may be wrong. Like FLT. Right?    					   
Newsgroups: sci.math
From: sundar+@cs.cmu.edu (Sundar Vallinayagam)
Subject: Re: A simple (?) integral
Organization: School of Computer Science, Carnegie Mellon
Date: Sun, 10 Jan 1993 21:01:01 GMT


>Considering 1,000,000 minds are better than one, I thought I'd post this
>wonderful problem...
>
>  _    ______
> (    /
> _) `/ tan x   dx
>
>
>Obviously the normal substution t=tan(x/2) won't work since this is no a
>rational function of since and cosine, and integration by parts doesn't
>look too promising...
>
>Mail ranging from insight to a solution, a complete solution, or this is
>not integrable in elementary functions because ________ would be greatly
>appreciated...
>
>Thank you.

Couldn't resist replying to this one.  So here goes:

       2
Let   t   =  tan x

                2
Then 2t dt = sec x dx

                     2
           = (1 + tan x) dx

                 4
           = (1+t ) dx

                      4
or   dx =    2t / (1+t )  dt

                           2        4
Therefore, I = integral  2t / (1 + t )  dt
            
               2         2      2 
Now express  2t  as  (1+t ) + (t -1) and split the integral into two parts
and divide by t^2 throughout.

That is:

                        2                  2
                   1+1/t              1-1/t
      integral   ----------    +   ------------   dt
                    2     2            2     2
                   t + 1/t            t + 1/t


Make the substitution  t - 1/t = u for the first term and

                       t + 1/t = v for the second term.


The integral now becomes:


  
                      du                       dv
      integral   ------------  +  integral -----------
                     2                       2
                    u  + 2                  v  - 2


Beyond this point, I have absolutely no clue as to how to proceed :-)


ramli.

PS: I first encountered this problem when I was in the 12th grade...



-- 
**************************************************
ramli@orca.ele.uri.edu
**************************************************
From: jack@dcs.glasgow.ac.uk (Jack Campin)
Newsgroups: sci.math
Subject: Re: math dictionary
Date: 8 Jan 93 16:24:06 GMT
Reply-To: jack@dcs.glasgow.ac.uk (Jack Campin)
Organization: COMANDOS Project, Glesga Yoonie

glenne@csd4.csd.uwm.edu (Neuromancer ) wrote:
> I bought _The Penguin DICTIONARY OF MATHEMATICS_.  Many times I find the
> definitions either too cryptic or lacking enough explanation.  Does anyone
> know of a mathematical dictionary for idiots that still contains useful
> and comprehensive information?

Not quite "for idiots", but at only a slightly higher level than the Penguin,
about the same size, and vastly better in its explanations: the French
"Dictionnaire des mathematiques modernes" (published by Larousse, I think).
There's no English translation that I know of, but the French is not overly
complicated.

My usual quick test for a mathematics dictionary is to look up "tensor".
This one emerges way ahead of its rivals on that.  The Penguin is a total
flop.

-- 
--  Jack Campin    room G092, Computing Science Department, Glasgow University,
17 Lilybank Gardens, Glasgow G12 8RZ, Scotland   TEL: 041 339 8855 x6854 (work)
INTERNET: jack@dcs.glasgow.ac.uk or via nsfnet-relay.ac.uk    FAX: 041 330 4913
BANG!net: via mcsun and uknet     BITNET: via UKACRL    UUCP: jack@glasgow.uucp
Newsgroups: sci.math
From: shallit@graceland.uwaterloo.ca (Jeffrey Shallit)
Subject: Lunde's problem (least number with n divisors)
Keywords: unique factors
Organization: University of Waterloo
Date: Mon, 4 Jan 1993 13:15:37 GMT

In article <1993Jan3.003521.26610@tessi.com> ronl@tessi.com (Ron Lunde) writes:
>I'm not a mathematician, so I'd appreciate it if anyone could point me to
>any references on this topic (that I might be able to understand :-)).
>
>The question I was toying with last night was: Given a number N,
>what is the smallest number M such that aside from 1 and M, M has exactly
>N unique factors (I guess I'm probably using "factor" in a funny way here,
>since I'm not referring to primes, necessarily).  Obviously there *is* such
>a number, since we can construct at least one by multiplying the first N
>primes.  It seems odd that the first ones are all fairly small, but I can't
>find the 15th (at least nothing smaller than 614889782588491410):
>
>N Divisors Smallest M  Factors
>2          6           2, 3
>3          16          2, 4, 8
>4          12          2, 3, 4, 6
>5          64          2, 4, 8, 16, 32
>6          24          2, 3, 4, 6, 8, 12
>7          36          2, 3, 4, 6, 9, 12, 18
>8          48          2, 3, 4, 6, 8, 12, 16, 24
>9          1024        2, 4, 8, 16, 32, 64, 128, 256, 512
>10         60          2, 3, 4, 5, 6, 10, 12, 15, 20, 30
>11         4096        2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048
>12         192         2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96
>13         144         2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72
>14         120         2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60
>
>Anyone know about this?
>Thanks!
>
>Ron Lunde
>email: ronl@tessi.com

Basically, you're looking for the smallest integer M with n positive *divisors*
(although most mathematicians would include 1 and M in the enumeration).

This problem has not been extensively studied, to my knowledge.  The sequence
is #A5179 in the new version of Sloane's book (which has yet to appear).  The
only reference I know is Beiler, Recreations in the Theory of Numbers, pp. 7-8.
Beiler also sketches an algorithm that will find such numbers.   To the best
of my knowledge, it is not known how to produce the prime factorization of
the solution in polynomial time (in log n, of course).  It is clearly impossible,
in general, to produce the (say base-10) expansion of the solution in polynomial
time in log n, since in general it could have Theta(n) digits.

The least number with 17 divisors (or 15, using your definition) is 2^16.

Jeff Shallit
Newsgroups: sci.math
From: seeta@eng.wayne.edu (Seetamraju UdayaBhaskar Sarma)
Subject: Re: proof wanted
Reply-To: seeta@eng.wayne.edu
Organization: College of Engineering, Wayne State University, Detroit Michigan, USA
Date: Tue, 12 Jan 1993 00:59:11 GMT

In article 1595@cc.umontreal.ca, cazelaig@ERE.UMontreal.CA (Cazelais Gilles) writes:
-+>i.e. such that:   |x-c'| >= |x-c| for all c' in C.
-+>
-+>If it is true I would appreciate if someone could give me a proof 
-+>of the result.


I have read all the responses, especially those that have branched off
in dealing with metric spaces.

I have seen proofs for what was asked, made for hilbert/banach spaces.  Given the
rich proerpties of these hilbert & banach spaces, how realistic is it
to expect similar behaviour for arbitrary metric spaces, which do not
(having seen many examples on this topic) even posses basic linear
space properties ?

Many of the metric spaces constructed, were bare-bones metric spaces, and that's it.
At most, they possessed A SINGLE converging sequence.  I personally thought
the argument had little worthwhile-ness...

How about basic linear space with discrete structure, but infinite size...
I think a infinte continuous linear space case is well studied...

Seetamraju Udaya Bhaskar Sarma
(email : seetam @ ece7 . eng . wayne . edu)

P.S.  I know as much of this topic, as luenberger's book on functional and
vector space analysis tells me...
Newsgroups: sci.math
From: rivin@SAIL.Stanford.EDU (Igor Rivin)
Subject: Re: sci.math: Frequently Asked Questions
Organization: Computer Science Department,  Stanford University.
Date: Tue, 12 Jan 1993 20:31:18 GMT


In article <1iuffrINN8v5@sol.deakin.OZ.AU> huang@deakin.OZ.AU (Weiguang Huang) writes:
>	As pointed out many times, this "FAQ" misses many symbolic
>computation packages in the list of the packages (6Q). "This is not
>a comprehensive list", but the list is the "FAQ" list so the list should
>include the popular packages, otherwise how can you claim yours is FAQ ?
>The following are some of these popular packages:
>
>[...disguised SymbMath plug, in the form of an old list of obscure math
>programs,  omitted...]

FAQ = Frequently Asked Questions.

If FAQ meant Frequently Answered Questions, I would be the first to
agree that SymbMath should have been at the top of the list.
Newsgroups: sci.math
From: bs@gauss.mitre.org (Robert D. Silverman)
Subject: Re: Let's add some sci.math.* groups
Organization: Research Computer Facility, MITRE Corporation, Bedford, MA
Date: Mon, 11 Jan 1993 14:22:29 GMT

In article <1993Jan11.132922.3391@news.unige.ch> swann@divsun.unige.ch (SWANN philip) writes:
>I support this idea!


I vote a resounding  NAY.

Mathematics is getting too specialized as it is. Let's not make it 
worse.

I *might* vote for a split into sci.math, and sci.math.recreational,
as well as keeping sci.math.research.

--
Bob Silverman
These are my opinions and not MITRE's.
Mitre Corporation, Bedford, MA 01730
"You can lead a horse's ass to knowledge, but you can't make him think"
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
Date: 5 Jan 1993 20:10:46 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In articles <> several well-meaning but misguided souls write:

>Have they suddenly lost the ability to use the libraries?

Just how many copies of a text book do you suppose a library carries?
(None. If they find out it's a text, they hide it so it won't be stolen.)
And if you're so lucky as to be the first to find it, how long will it
be before someone else puts a hold on it and you're forced to give it
up? ( 4 weeks.)

> The idea that some are going without food is ridiculous.

No it isn't.  I can't imagine a time in my future when I will cease to be 
bitter about the ignorant comments made by middle-class frat boys who've
had everything handed to them on a silver-plated platter.

Very, very sincerely,
Bart Goddard
From: np4@prism.gatech.EDU (Nick Pomponio)
Newsgroups: sci.math
Subject: Constant-sum table algorithm
Date: 8 Jan 93 12:49:33 GMT
Organization: Georgia Institute of Technology

I would like to generate an NxN table of positive integers such that
any N entries chosen from the table, with the restriction that no
two in are in the same row or column, add up to the same value, S.
The only way I know to construct such a table is to choose 2N integers
which sum to S, arrange N along the top of the table (one above each
column), and N along the side (one beside each row), then fill in each
entry as the sum of it's corresponding row and column heading numbers.

Question: Is there an algorithm for choosing the 2N integers such that
every resulting number in the NxN table is unique (no repetitions)?
For my particular case, N^2 << S.

Thanks.

-- 
POMPONIO,NICHOLAS A
Georgia Institute of Technology, Atlanta Georgia, 30332
uucp:	  ...!{decvax,hplabs,ncar,purdue,rutgers}!gatech!prism!np4
Internet: np4@prism.gatech.edu
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Subsidizing Education
Date: 7 Jan 93 16:17:05 GMT
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Organization: Computer Science Department at Rose-Hulman
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

I have another (sorry) tangent for the "Textbook" thread.  I have no data to  
back up or gainsay what the following implies, but if anyone does...:

I read an article years ago by an author.  He said that he had won some sort of  
writing scholarship from the government in high school which allowed him to  
attend some prestigious school and study writing.  He graduated and has since  
caused millions of books to be sold, and, he figured, thereby generated $(some  
large number) of tax revenue.  Hence the government's investment in his  
education was returned mega-fold.

--
Bart Goddard   
Math. Dept. Rose-Hulman Inst. of Tech.
goddard@nextwork.rose-hulman.edu
Newsgroups: sci.math
From: swsy@next4 (STEVEN W. SY)
Subject: Re: A simple (?) integral
Organization: Michigan Technological University
Date: Sun, 10 Jan 1993 19:54:20 GMT

Mark Spaeth asked:


>Considering 1,000,000 minds are better than one, I thought I'd post this
>wonderful problem...
>
>  _    ______
> (    /
> _) `/ tan x   dx
>
>
>Obviously the normal substution t=tan(x/2) won't work since this is no a
>rational function of since and cosine, and integration by parts doesn't
>look too promising...
>
>Mail ranging from insight to a solution, a complete solution, or this is
>not integrable in elementary functions because ________ would be greatly
>appreciated...


I found that if I used a u=tan x substitution, I could reduce the integral
to:

  _  u^(1/2)  
 (   _______ du
 _)  u^2 + 1


This integral was more easily solvable.  This form can be solved by
Mathematica.
The complete solution is:

{{Arctan[1+Sqrt[2*Tan(x)]]}/Sqrt(2)}
-{{Arctan[1-Sqrt[2*Tan(x)]]}/Sqrt(2)}
+{{Ln[1-Sqrt[2*Tan(x)]+Tan(x)]}/(2*Sqrt(2))}
-{{Ln[1+Sqrt[2*Tan(x)]+Tan(x)]}/(2*Sqrt(2))}

Enjoy!
------------------------------------------------------------------------
"2+2=4.  If that is granted, all else follows"--George Orwell
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Fields Medal Winners
Date: 10 Jan 93 15:46:40 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1993Jan10.003051.11353@infodev.cam.ac.uk> crb11@cus.cam.ac.uk (Colin Bell) writes:

>The Tripos is an exclusively Cambridge object: it's alive and reasonably well.
>Hardy didn't get it abolished, merely reformed (this was in 1910). 

Just So.

>Since then,
>it's spread to other subjects apart from mathematics (in fact all other
>undergraduate exams are now Tripos).   

Sorry to hear it, but thanks for the clarification. Although I believe
exams when sensibly used are necessary and can be a positive thing, I
am essentially implacably opposed to mathematics tests which have
high publicity results. This applies equally to the blithering drones
of Mensa etc. as to the slightly less narrow visions of mathematics
competitions.

Later,
Andrew Mullhaupt
From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Looking for help
Date: 9 Jan 93 18:25:59 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1993Jan8.150941.12619@infodev.cam.ac.uk> cet1@cus.cam.ac.uk (C.E. Thompson) writes:
>In article <1444@kepler1.rentec.com>, andrew@rentec.com (Andrew Mullhaupt) writes:
>|> In article <1993Jan4.140128.20155@choate.edu> jburne@spock.uucp (John Burnette)
>|> writes:
>|> >"Give two numbers, x and y, whose sum is rational and whose product is 
>|> >irrational."
 
>|> >x = .10100100010000....
>|> >y = .01011011101111....
 
>|> >Obviously x+y=1/9 (and, please, let's not start that thread again...)
>|> >but I've always been at a lost about x*y.
 
>|> It isn't entirely clear but I suppose that x is a Liouville* number, in
>|> which case it is transcendental.

>It wasn't explicitly stated, but I took the chains of zeroes to be increasing
>linearly in size, i.e. x = \sum_{n=1}^{\infty} 10^{-n(n+1)/2}. In which case
>the gaps aren't big enough to make the rational approximations with denominator
>10^{n(n+1)/2} convergents to x, let alone make it a Liouville number.

>|> *Or a Thue-Siegel-Roth number, etc.

>Same applies.

Well if you want to talk about _that_ number life is indeed much more
difficult. As I said, it isn't clear which number was originally given,
so I gave the student the benefit of the doubt. But things can be done
with the number you think x is. As noted in my previous post, the
only way for x * (1/9 - x) to be rational with x irrational is for x to
be a quadratic irrationality. By Euler-Lagrange, the continued fraction
of such x will be periodic. If we put x = sum 10 ^ ((-n^2-n)/2) as you
suggest, we get the continued fraction:

	x = [0,9,1,9,11,9,11,90,1,9,1,90,110,9,12,4,1,3,1,4,2,1,4,4,10,
	     1,10,9,907,2,1,2,6,3,1,4,1,9...]

which does not appear to have a periodicity. We should not expect the
continued fraction of x to be _purely_ periodic, since x < 1, but
eventually periodic.

Later,
Andrew Mullhaupt

P.S. I think you can get a handle on your number x using the theta
functions, and then known transcendence results (Cf. Baker's 
_Transcendental Number Theory_) may apply, but I don't have time to chase
this down.
From: sauloy@tls-cs.cert.fr (Jacques Sauloy)
Newsgroups: sci.math
Subject: Re: non-enumerable well ordered sets
Keywords: any *explicit* example ?
Date: 7 Jan 93 11:22:06 GMT
Organization: CERT Toulouse Dept of Computer Science, FRANCE

(OOOOPS)
nypardon me for the P.S. to my previous question : since the discrete order on any set (i.e. equality) is always artinian, the question is trivial . However, I think questions 1 and 2 are not.
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
Newsgroups: sci.math
Subject: Re: High Prices of Math Books. I am pissed.
Date: 6 Jan 1993 18:56:14 GMT
Organization: Computer Science Department at Rose-Hulman
Reply-To: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
NNTP-Posting-Host: g214-1.nextwork.rose-hulman.edu

In article <1idj1gINNhah@roundup.crhc.uiuc.edu> hougen@focus.csl.uiuc.edu  
(Darrell Roy Hougen) writes:
> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:
> 
> % In articles <> several well-meaning but misguided souls write:
> %% Have they suddenly lost the ability to use the libraries?
> % Just how many copies of a text book do you suppose a library carries?
> 
> You said that college students didn't have the opportunity to read,
> *not* just that text books were expensive. 

That wasn't me.

>[...] 
> 
> Darrell R. Hougen

Just to clear things up a bit, MY only contribution is to say that people
who don't know how hard it is to get through undergraduate school without 
enough money should shut up and quit saying "let them eat cake."

Some of us DID have to do without food, movies, beer (yes, even I), going home 
(or anywhere) during spring break, phone calls, laundry soap, condoms, etc.   
When we say so, it is extremely arrogant to say that it is "nonsense" or  
"ridiculous".  

We are not complaining about our LOT.  What we resent are COMMENTS that  
belittle or dismiss our effort, especially by folks who really have no idea  
what it's like to spend a week on a deserted campus during spring break or
Thanksgiving.

bart
From: martin@lyra.cis.umassd.edu (Gary Martin)
Newsgroups: sci.math
Subject: Re: spell this?
Date: 12 Jan 93 04:31:44 GMT
Organization: University of Massachusetts Dartmouth

In article <1isvrsINNe11@master.cs.rose-hulman.edu> goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard) writes:

   The raging debate here is the correct spelling of (choose one and 
   supply a reference):

   a) nilpotentcy
   b) nilpotency
   c) other

   As in "the degree of nilpotency of a thing."

I'm sure that c) is the correct spelling of 'other'.  As for the choice
between a) and b), I'd have to say that  a) looks terribly awkward.
The OED lists "potency" but not "potentcy", which pretty much convinces
me.


--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Martin@cis.umassd.edu
From: delgado@elm.egr.msu.edu (Richard Delgado)
Newsgroups: sci.math
Subject: Surface Fitting
Date: 12 Jan 93 17:19:04 GMT
Organization: College of Engineering, Michigan State University
NNTP-Posting-Host: elm.egr.msu.edu


	I would appreciate any information on software packages, preferably
shareware, that can find coefficients given a model and a data set. The data
is to be 3-d i.e. z as a function of x and y. Please respond with e-mail.

Thanks in advance.
-- 
///////////////////////////////////////////////////////////////////////////////

     //////                    //          Rick Delgado
    //   //                   // //        delgado@egr.msu.edu
   //////    //    //////    ////          Dept. of Chemical Engr.
  // //     //    //        // //          Michigan State University
 //  //    //    //////    //   //

///////////////////////////////////////////////////////////////////////////////
Newsgroups: sci.math
From: kavuri@lips1.ecn.purdue.edu (Surya N Kavuri )
Subject: sum of eigenvalues of a covariance matrix = trace ?
Organization: Purdue University Engineering Computer Network
Date: Sat, 9 Jan 1993 19:48:45 GMT

  Is the sum of the eigenvalues of a covariance matrix equal to 
   its trace ?

 Surya Kavuri