Given any inner product (,) on a vector space, we can define a norm by ||x||...

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Given any inner product (,) on a vector space, we can define a norm by ||x|| = (x, x) 1/2. The converse is not true, i.e., there are norms that are not induced by an inner product. Show that the infinity norm ||-|| for vectors in R" is not induced by any inner product when n 2. Given any inner product (,) on a vector space, we can define a norm by ||x|| = (x, x) 1/2. The converse is not true, i.e., there are norms that are not induced by an inner product. Show that the infinity norm ||-|| for vectors in R" is not induced by any inner product when n 2.