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A vector space $S$ with a valid inner product defined on it is called an inner product space , which is also a normed linear space . A Hilbert space is an inner product space that is complete with respect to the norm defined using the innerproduct. Hilbert spaces are named after David Hilbert , who developed this idea through his studies of integral equations. We define our valid norm using the innerproduct as:
Below we will list a few examples of Hilbert spaces . You can verify that these are valid inner products at home.
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