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Topic: Simple (?) matrix proof
Replies: 50   Last Post: Sep 21, 2009 9:56 AM

 Messages: [ Previous | Next ]
 Dik T. Winter Posts: 7,899 Registered: 12/6/04
Re: Simple (?) matrix proof
Posted: Sep 18, 2009 10:43 AM

In article <f0237a42-1f0c-43a4-8d9c-c05ff7eb2939@p36g2000vbn.googlegroups.com> un student <un.student@gmail.com> writes:
> On Sep 18, 4:21=A0pm, Maarten Bergvelt <be...@math.uiuc.edu> wrote:
...
> > and you know that
> > for all x,y you have <x,Ay>=3D0. Well, what does A=3D0 mean? It means that
> > all the matrix coefficients a_{ij} are zero. But we can choose x, y to
> > be the standard basis vectors e_i, e_j. Then <e_i, Ae_j>=3Da_ij, so this
> > coefficient is zero. Then repeat for all i and j to conclude that
> > A=3D0.

>
> Yep, so we can choose x,y so that A must be zero and this is enough to
> show that it follows for any x and y A=0?

No, you choose x and y so that you prove that a particular entry of A equals
0. And for each entry of A you can chose such x and y. And if all entries
are 0, the matrix itself is 0. Being 0 or not is not something that depends
on the things you multyply it with.
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Date Subject Author
9/18/09 un student
9/18/09 J. Antonio Perez M.
9/18/09 J. Antonio Perez M.
9/18/09 un student
9/18/09 J. Antonio Perez M.
9/18/09 un student
9/18/09 Maarten Bergvelt
9/18/09 un student
9/18/09 Timothy Murphy
9/18/09 un student
9/18/09 J. Antonio Perez M.
9/18/09 Maarten Bergvelt
9/18/09 The Qurqirish Dragon
9/18/09 Dik T. Winter
9/18/09 un student
9/18/09 un student
9/18/09 J. Antonio Perez M.
9/18/09 un student
9/19/09 un student
9/19/09 Maarten Bergvelt
9/19/09 Ted Hwa
9/19/09 un student
9/19/09 J. Antonio Perez M.
9/19/09 Maarten Bergvelt
9/19/09 un student
9/19/09 un student
9/19/09 Maarten Bergvelt
9/19/09 J. Antonio Perez M.
9/19/09 Maarten Bergvelt
9/20/09 un student
9/20/09 Maarten Bergvelt
9/20/09 un student
9/20/09 J. Antonio Perez M.
9/19/09 Ki Song
9/20/09 J. Antonio Perez M.
9/20/09 Ted Hwa
9/20/09 un student
9/20/09 Maarten Bergvelt
9/20/09 un student
9/20/09 Maarten Bergvelt
9/20/09 un student
9/20/09 J. Antonio Perez M.
9/21/09 un student
9/21/09 J. Antonio Perez M.
9/21/09 Maarten Bergvelt
9/20/09 David Hartley
9/20/09 un student
9/20/09 Stephen J. Herschkorn
9/20/09 Stephen J. Herschkorn
9/18/09 Dave Dodson
9/18/09 The Qurqirish Dragon