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Topic: [HM] possible Hilbert quote?
Replies: 39   Last Post: Apr 19, 2002 10:09 AM

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Prof. S.D. Agashe

Posts: 30
Registered: 12/3/04
[HM] A "linear algebra" result
Posted: Apr 19, 2002 10:09 AM
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I came across the following "linear algebra" result recently:

(Source: Vector Calculus, by Durgaprasanna Bhattacharyya, University
Studies Series,Griffith Prize Thesis, 1918, published by the University
of Calcutta, India, 1920, 90 pp)

Chapter IV: The Linear Vector Function, article 15, p.24:

"The most general vector expression linear in r can contain terms only
of three possible types, r, (a.r)b and cxr, a, b, c being constant unit
vectors. Since r, (a.r)b and cxr are in general non-coplanar,it follows
from the theorem of the parallelepiped of vectors that the most general
linear vector expression can be written in the form

lambda r + mu (a.r)b + nu cxr

where lambda, mu, nu are scalar constants".

Bhattacharyya does not prove this. Has anyone seen a similar result
and its proof?

Bhattacharyya uses this to show that the divergence of the linear
function is (3 lambda + a.b), that the curl is (axb + 2c). He goes on
to define div and curl of a differentiable function as the div and
curl of the (linear) derivative function. The div and curl of a linear
function are defined in terms of certain surface integrals.

I am excited about this result because it seems to provide an excellent
route to div and curl, as Bhattacharyya himself remarks.

Sorry for a rather long and "technical" communication.

S D Agashe, from a humid Mumbai





Date Subject Author
4/2/02
Read [HM] possible Hilbert quote?
John Mason
4/2/02
Read Re: [HM] possible Hilbert quote?
George Matthews
4/2/02
Read [HM] Dubitability and Euclid's fifth postulate
Richard Grandy
4/3/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Christian Marinus Taisbak
4/3/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Roger Cooke
4/4/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Laura Elena Morales Gro.
4/6/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Nimish Shah
4/7/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Samuel S. Kutler
4/11/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Dr. Siegmund Probst
4/8/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
James A Landau
4/10/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Samuel S. Kutler
4/12/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
John Conway
4/12/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
David Stump
4/14/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
John Conway
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Emili Bifet
4/17/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Emili Bifet
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Nimish Shah
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Matt Insall
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Laura Elena Morales Guerrero
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
John Conway
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Laura Elena Morales Guerrero
4/15/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Samuel S. Kutler
4/16/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
John Conway
4/16/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Gordon Fisher
4/17/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Matt Insall
4/16/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Laura Elena Morales Guerrero
4/16/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Laura Elena Morales Guerrero
4/16/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Nimish Shah
4/11/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Franz Lemmermeyer
4/11/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Roger Cooke
4/13/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
James A Landau
4/14/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
John W. Dawson, jr.
4/16/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
James A Landau
4/18/02
Read Re: [HM] Dubitability and Euclid's fifth postulate
Tony Maric
4/19/02
Read [HM] A "linear algebra" result
Prof. S.D. Agashe
4/3/02
Read Re: [HM] possible Hilbert quote?
Jose Ferreiros
4/3/02
Read Re: [HM] possible Hilbert quote?
Martin Davis
4/5/02
Read Re: [HM] possible Hilbert quote?
Emili Bifet
4/5/02
Read Re: [HM] possible Hilbert quote?
Augusto Oliveira
4/5/02
Read Re: [HM] possible Hilbert quote?
Augusto Oliveira

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