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inner product::noun | Spocien Dictionary
| Type | Words |
|---|---|
| Synonyms | dot product, scalar product |
| Type of | real, real number |
Examples of inner product
inner product
A vector space equipped with a scalar product is called an inner product space.
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A vector space with a bilinear form generalizes the case of an inner product.
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The complex absolute value is a special case of the norm in an inner product space.
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The dot product is called the standard inner product or the Euclidean inner product.
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In particular, two vectors are considered orthogonal if their inner product is zero.
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An important example is a Hilbert space, where the norm arises from an inner product.
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The inner product space is called a Hilbert space if its associated norm is complete.
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However, one can still define generalized rotations which preserve this inner product.
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Here we introduce a nonnegative weight function in the definition of this inner product.
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