Mathematics · Functional Analysis
If ||·|| is a norm generated by an inner product on a vector space V, then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1||x + y||2 = ||x||2 + ||y||2 for all x, y ∈ V
- 2||x + y||2 + ||x - y||2 = 2||x||2 + 2||y||2 for all x, y ∈ V✓
- 3||x + y||2 = 2||x||2 + 2||y||2 for all x, y ∈ V
- 4||x + y||2 + ||x - y||2 = 2||x||2 for all x, y ∈ V
Correct answer
||x + y||2 + ||x - y||2 = 2||x||2 + 2||y||2 for all x, y ∈ V
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