3.10 Show that a norm ||-|| on a linear space X is generated by a scalar...

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3.10 Show that a norm ||-|| on a linear space X is generated by a scalar product if and only if the parallelogram equality ||x+y||²+ ||xy||² = 2(||*||² + ||y||²) holds for all x, y EX. Show that the ₁ and loo norms on C" are not generated by scalar products. 3.10 Show that a norm ||-|| on a linear space X is generated by a scalar product if and only if the parallelogram equality ||x+y||²+ ||xy||² = 2(||*||² + ||y||²) holds for all x, y EX. Show that the ₁ and loo norms on C" are not generated by scalar products.

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A norm on a linear space X is generated by a scalar product if and only if the parallelogram ... View the full answer