inner product

Noun

Meaning

a real number (a scalar) that is the product of two vectors

Source: WordNet

Synonyms

Hypernyms

Examples

For the p -norm becomes the Euclidean norm: :: :which is Pythagoras' theorem in n -dimensions, a very special case corresponding to an inner product norm. Source: Internet

Any complete inner product space V has an orthonormal basis. Source: Internet

Curl geometrically 2-vectors correspond to the exterior power ; in the presence of an inner product, in coordinates these are the skew-symmetric matrices, which are geometrically considered as the special orthogonal Lie algebra of infinitesimal rotations. Source: Internet

Direct sum of modules with additional structure If the modules we are considering carry some additional structure (e.g. a norm or an inner product ), then the direct sum of the modules can often be made to carry this additional structure, as well. Source: Internet

Every inner product V space is a dense subspace of some Hilbert space. Source: Internet

For example, a bilinear form is the same thing as a (0, 2) -tensor; an inner product is an example of a (0, 2) -tensor, but not all (0, 2) -tensors are inner products. Source: Internet

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