Polarization identity for real inner space

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Theorem 2 (Polarization Identity) Suppose V is an inner product space with an inner product (·,·) and the induced norm ‖·‖. (i) If V is a real vector space, then for any x,y ∈ V, ... (ii) If V is a complex vector space, then for any x,y ∈ V, (x,y) = 1 4( ‖x + y‖2 − ‖x − y‖2 + i‖x + iy‖2 − i‖x − iy‖2).

Polarization identity for real inner space

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