inner product
in·ner prod·uct
I i Transcription
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- US Pronunciation
- US IPA
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- [in-er prod-uh kt, -uhkt]
- /ˈɪn ər ˈprɒd əkt, -ʌkt/
-
- US Pronunciation
- US IPA
-
- [in-er prod-uh kt, -uhkt]
- /ˈɪn ər ˈprɒd əkt, -ʌkt/
Definitions of inner product words
- noun inner product Also called dot product, scalar product. the quantity obtained by multiplying the corresponding coordinates of each of two vectors and adding the products, equal to the product of the magnitudes of the vectors and the cosine of the angle between them. 1
- noun inner product the integral of the product of two real-valued functions. 1
- noun inner product the integral of the product of the first of two complex-valued functions and the conjugate of the second. 1
- noun inner product a complex-valued function of two vectors taken in order, whose domain is a vector space. 1
- noun Technical meaning of inner product (mathematics) In linear algebra, any linear map from a vector space to its dual defines a product on the vector space: for u, v in V and linear g: V -> V' we have gu in V' so (gu): V -> scalars, whence (gu)(v) is a scalar, known as the inner product of u and v under g. If the value of this scalar is unchanged under interchange of u and v (i.e. (gu)(v) = (gv)(u)), we say the inner product, g, is symmetric. Attention is seldom paid to any other kind of inner product. An inner product, g: V -> V', is said to be positive definite iff, for all non-zero v in V, (gv)v > 0; likewise negative definite iff all such (gv)v < 0; positive semi-definite or non-negative definite iff all such (gv)v >= 0; negative semi-definite or non-positive definite iff all such (gv)v <= 0. Outside relativity, attention is seldom paid to any but positive definite inner products. Where only one inner product enters into discussion, it is generally elided in favour of some piece of syntactic sugar, like a big dot between the two vectors, and practitioners don't take much effort to distinguish between vectors and their duals. 1
- noun inner product (linear algebra) A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered. 0
Information block about the term
Origin of inner product
First appearance:
before 1915 One of the 14% newest English words
First recorded in 1915-20
Historical Comparancy
Parts of speech for Inner product
noun
adjective
verb
adverb
pronoun
preposition
conjunction
determiner
exclamation
inner product popularity
A pretty common term. Usually people know it’s meaning, but prefer to use a more spread out synonym. About 31% of English native speakers know the meaning and use word.
According to our data about 61% of words is more used. This is a rare but used term. It occurs in the pages of specialized literature and in the speech of educated people.
inner product usage trend in Literature
This diagram is provided by Google Ngram ViewerSynonyms for inner product
noun inner product
- dot product — inner product (def 1).
See also
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