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Forum index » Science and Technology » Math
Rank of a matrix with bounded elements
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eugene
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Joined: 24 Nov 2005
Posts: 331

PostPosted: Sat Jul 15, 2006 7:46 am    Post subject: Rank of a matrix with bounded elements Reply with quote
Let A be an nxn symmetric real matrix with a_ii = 1 for all 1 <= i <= n
and |a_ij| < 1/sqrt(n) for all i <> j. How can one prove that A has
rank at least r . What do you think : is this bound optimal ?

Thanks
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Simple
science forum beginner


Joined: 15 Jul 2006
Posts: 3

PostPosted: Sat Jul 15, 2006 8:29 am    Post subject: Re: Rank of a matrix with bounded elements Reply with quote
to make all elements below the diagonal 0, you can find that every one in
the diagonal is still positive


"eugene" <jane1806@rambler.ru>
??????:1152949578.666709.76440@m73g2000cwd.googlegroups.com...
Quote:
Let A be an nxn symmetric real matrix with a_ii = 1 for all 1 <= i <= n
and |a_ij| < 1/sqrt(n) for all i <> j. How can one prove that A has
rank at least r . What do you think : is this bound optimal ?

Thanks
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Simple
science forum beginner


Joined: 15 Jul 2006
Posts: 3

PostPosted: Sat Jul 15, 2006 8:29 am    Post subject: Re: Rank of a matrix with bounded elements Reply with quote
to make all elements below the diagonal 0, you can find that every one in
the diagonal is still positive


"eugene" <jane1806@rambler.ru>
??????:1152949578.666709.76440@m73g2000cwd.googlegroups.com...
Quote:
Let A be an nxn symmetric real matrix with a_ii = 1 for all 1 <= i <= n
and |a_ij| < 1/sqrt(n) for all i <> j. How can one prove that A has
rank at least r . What do you think : is this bound optimal ?

Thanks
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eugene
science forum Guru


Joined: 24 Nov 2005
Posts: 331

PostPosted: Sat Jul 15, 2006 9:54 am    Post subject: Re: Rank of a matrix with bounded elements Reply with quote
eugene wrote:
Quote:
Let A be an nxn symmetric real matrix with a_ii = 1 for all 1 <= i <= n
and |a_ij| < 1/sqrt(n) for all i <> j. How can one prove that A has
rank at least r . What do you think : is this bound optimal ?

Thanks

Edited: Let A be an nxn symmetric real matrix with a_ii = 1 for all 1
<= i <= n
and |a_ij| < 1/sqrt(n) for all i <> j. How can one prove that Ahas
rank at least n/2 . What do you think : is this bound optimal ?
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