Definition of Inner product

1. Noun. A real number (a scalar) that is the product of two vectors.

Exact synonyms: Dot Product, Scalar Product
Generic synonyms: Real, Real Number



Definition of Inner product

1. Noun. (linear algebra) A generalization of the dot product for vectors of any dimensionality that may or may not be complex-numbered. ¹

¹ Source: wiktionary.com

Lexicographical Neighbors of Inner Product

inner children
inner circle
inner cities
inner city
inner core
inner dental epithelium
inner diameter
inner diameters
inner ear
inner ears
inner malleolus
inner membrane
inner peace
inner planet
inner planets
inner product (current term)
inner products
inner regular
inner resources
inner salt
inner sheath
inner strength
inner table of skull
inner tube
inner tubes
inner workings
innerbelt
innerbelts
innercity
innerduce

Literary usage of Inner product

Below you will find example usage of this term as found in modern and/or classical literature:

1. Analytic Statistical Models by Ib M. Skovgaard (1990)
"A real vector space equipped with an inner product is called a Euclidean space. ... Similarly we shall speak, slightly incorrectly, of an inner product ..."

2. The Theory of General Relativity and Gravitation: Based on a Course of by Ludwik Silberstein (1922)
"The outer multiplication combined with contraction (when there are indices to contract) gives the inner product. Thus the inner product of At and B" is ..."

3. Cartanian Geometry, Nonlinear Waves, and Control Theory. by Robert Hermann (1980)
"8.6 determines the inner product completely in inn BF ( ... be a real vector space with a positive definite inner product < , > • There is another Vector ..."

4. The Theory of the Relativity of Motion by Richard Chace Tolman (1917)
"inner product of Vectors in General. We have previously defined the inner ... We may now give a general rule for the inner product of vectors of any number ..."

5. The Encyclopaedia Britannica: A Dictionary of Arts, Sciences, Literature and (1910)
"The symbol AB, from this point of view, is called the inner product of A and B, ... An inner product may be either progressive or regressive. ..."

6. Real Analysis by Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson (1997)
"Specifically, then, a Hilbert space is an inner product space that is ... Notice first the linearity of an inner product in the first variable: (Ai/i + A2/2 ..."

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