If V = U ⊕ U⟂ and V = W ⊕ W⟂, and if S1: U...

If V = U ⊕ U^⟂ and V = W ⊕ W^⟂, and if S₁: U → W and S₂: U^⟂ → W^⟂ are isometries, then the linear operator defined for u₁ ∈ U and u₂ ∈ U^⟂ by the formula S(u₁ + u₂) = S₁u₁ + S₂u₂ is a well-defined linear isometry. Prove this.

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Colby Messinger answered 1 year ago

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