(b) Let V be a Hermitian inner product space over C, equipped with the Hermitian inner product (, ). Prove or disprove:

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B Let V Be A Hermitian Inner Product Space Over C Equipped With The Hermitian Inner Product Prove Or Disprove 1 (82.22 KiB) Viewed 40 times

(b) Let V be a Hermitian inner product space over C, equipped with the Hermitian inner product (, ). Prove or disprove: (i) for all ủ, Ủ e V, if lũ – ol = lũ + ill, then ủ and Ủ are orthogonal. ||ù v|| v||, (ii) if L: V → V is a linear operator such that ||L(v)|| = ||7|| for all 7 € V, then (L(ù), L(v)) = (ù, v) for all u, v € V.