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ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4705 on D34: Inner product
Inner product with repeating argument is a real number
Formulation 0
Let I be an D1128: Inner product space over C such that
(i) , is the D34: Inner product in I
(ii) xI is a D1129: Vector in I
Then x,xR
Proofs
Proof 0
Let I be an D1128: Inner product space over C such that
(i) , is the D34: Inner product in I
(ii) xI is a D1129: Vector in I
By conjugate symmetry, we have x,x=¯x,x Thus, this result is a consequence of result R2413: Complex conjugate of real number.