Thread: Inner product space proof question

Prove that {u,v}=0 for all v belongs to V iff u=0.

{u,v}= u*v, where u* is conjugate of u

If u=0 then {u,v} is obviously 0.

now im not sure how to prove it the other way

If {u,v}=0 then u=0

u*v=0...

Thanks in advance

Originally Posted by firebio

Prove that {u,v}=0 for all v belongs to V iff u=0.

{u,v}= u*v, where u* is conjugate of u

If u=0 then {u,v} is obviously 0.

now im not sure how to prove it the other way

If {u,v}=0 then u=0

u*v=0...

Thanks in advance

Apparently you're using {u,v} to denote inner product... Anyway, if it is true that then this is true for as well, so apply now positiveness of inner product to get that it must be .

Tonio

Originally Posted by firebio

Prove that {u,v}=0 for all v belongs to V iff u=0.

{u,v}= u*v, where u* is conjugate of u

If u=0 then {u,v} is obviously 0.

now im not sure how to prove it the other way

If {u,v}=0 then u=0

u*v=0...

Thanks in advance

What is the conjugate in this case?