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 Post subject: inner productPosted: Fri, 29 Apr 2011 09:40:02 UTC
 Member

Joined: Wed, 27 Apr 2011 17:25:08 UTC
Posts: 14
hello every one
i have another question
if A belong to C ^(nxn),show that (x.Ay)=0 for all x,y belong to C^(n),then A=0
(x.Ay) denote dot product

my answer to this question is
there is an axiom which says:
X.X (> or =) to 0 with equality only for x=0
then when applying it to our question then
x:matrix and y:matrix A:matrix
then x,y are variables then A: must be zero to satisfy the answer
since the question didnot tell us that x is orthogonal to y

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 Post subject: Re: inner productPosted: Fri, 29 Apr 2011 09:56:58 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6068
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
goldgirl wrote:
hello every one
i have another question
if A belong to C ^(nxn),show that (x.Ay)=0 for all x,y belong to C^(n),then A=0
(x.Ay) denote dot product

my answer to this question is
there is an axiom which says:
X.X (> or =) to 0 with equality only for x=0
then when applying it to our question then
x:matrix and y:matrix A:matrix
then x,y are variables then A: must be zero to satisfy the answer
since the question didnot tell us that x is orthogonal to y

Let x=Ay. What can you say about Ay for every y?

_________________

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 Post subject: Re: inner productPosted: Fri, 29 Apr 2011 21:42:02 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9642
goldgirl wrote:
if A belong to C ^(nxn),show that (x.Ay)=0 for all x,y belong to C^(n),then A=0
(x.Ay) denote dot product

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