I'm revising for my final and I can't seem to prove this. If llx+yll=llx-yll then then Real parts are 0 hence <x,y>=0 But I can't prove it starting with <x,y> any help appreciated
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Originally Posted by Roland25 I'm revising for my final and I can't seem to prove this. If llx+yll=llx-yll then then Real parts are 0 hence <x,y>=0 But I can't prove it starting with <x,y> any help appreciated Since you mention the real part is 0 I assume that Remember that so if we square both sides we get and using the above identity we get
Originally Posted by Roland25 Prove <x,y>=0 iff llx+yll=llx-yll This is true if the scalar field is the real numbers, but not if it is the complex numbers. For example, |1+i| = |1–i|, but .
Originally Posted by Roland25 I'm revising for my final and I can't seem to prove this. If llx+yll=llx-yll then then Real parts are 0 hence <x,y>=0 But I can't prove it starting with <x,y> any help appreciated Suppose Suppose .... Originally Posted by Opalg This is true if the scalar field is the real numbers, but not if it is the complex numbers. For example, |1+i| = |1–i|, but . You're right, it is not true that the , but it is always true that the Real part of is zero.
Last edited by mr fantastic; May 9th 2009 at 06:38 PM. Reason: Merged posts
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