what is relation of inner product space with normed space?
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Answer:
The abstract spaces-metric spaces, normed spaces, and inner product spaces-are all examples of what are more generally called "topological spaces." These spaces have been given in order of increasing structure. That is, every inner product space is a normed space, and in turn, every normed space is a metric space...
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Answer:
Step-by-step explanation:
The abstract spaces-metric spaces, normed spaces, and inner product spaces-are all examples of what are more generally called "topological spaces." These spaces have been given in order of increasing structure. That is, every inner product space is a normed space, and in turn, every normed space is a metric space.
Inner Product Spaces
Functional analysis involves studying vector spaces where we additionally have the notion of size of an element (the norm), such spaces are known as normed spaces. Sometimes we will have an additional notion of an inner product which can be informally thought of as a way of giving an angle between elements. Of particular interest will be infinite dimensional spaces
A real or complex vector space in which each vector has a non-negative length, or norm, and in which every Cauchy sequence converges to a point of the space. Also known as complete normed linear space.
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