Denote standard inner product

  • Thread starter bernoli123
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  • #1
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if A [tex]\in[/tex] C nxn,show that (x,Ay)=0 for all x,y [tex]\in[/tex] C[n],
then A=0

(x,Ay) denote standard inner product on C[n]
 

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  • #2
chiro
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if A [tex]\in[/tex] C nxn,show that (x,Ay)=0 for all x,y [tex]\in[/tex] C[n],
then A=0

(x,Ay) denote standard inner product on C[n]

Have you tried using properties of norms, and axioms of the inner product (There is an axiom that deals with zero results)?
 
  • #3
HallsofIvy
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In particular, (e_i, Ae_i)= 0 for every member, [itex]e_i[/itex], of an orthonormal basis.
 
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