In mathematics, a vector space or function space in which an operation for combining two vectors or functions (whose result is called an inner product) is defined and has certain properties. Such spaces, an essential tool of functional analysis and vector theory, allow analysis of classes of functions rather than individual functions. In mathematical analysis, an inner product space of particular importance is a Hilbert space, a generalization of ordinary space to an infinite number of dimensions. A point in a Hilbert space can be represented as an infinite sequence of coordinates or as a vector with infinitely many components. The inner product of two such vectors is the sum of the products of corresponding coordinates. When such an inner product is zero, the vectors are said to be orthogonal (see orthogonality). Hilbert spaces are an essential tool of mathematical physics. See also David Hilbert,
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inner product space
In mathematics, a vector space or function space in which an operation for combining two vectors or functions (whose result is called an inner product) is defined and has certain properties. Such spaces, an essential tool of functional analysis and vector theory, allow analysis of classes of functions rather than individual functions. In mathematical analysis, an inner product space of particular importance is a Hilbert space, a generalization of ordinary space to an infinite number of dimensions. A point in a Hilbert space can be represented as an infinite sequence of coordinates or as a vector with infinitely many components. The inner product of two such vectors is the sum of the products of corresponding coordinates. When such an inner product is zero, the vectors are said to be orthogonal (see orthogonality). Hilbert spaces are an essential tool of mathematical physics. See also David Hilbert
Some etymologies, pronunciations, function and usage date content for the English translation portion are from Merriam-Webster Online at www.Merriam-Webster.com. Thanks to Online Yunanca Dil Eğitimi for providing some parts of online greek dictionary. To contribute more resources please contact us. Visuals(images) are provided by Google Image Search API. Some parts of the dictionary is contributed by many users, thank you! The content on this site is for informational purposes only. Bu aramada inner product spaces kelimesinin sözlük anlamı ve eşanlamı nedir, nasıl okunur hakkında bilgi verilmektedir. inner product spaces kelimesinin etimolojik ve eşanlamları ile ilgili açıklamalar ve bilgiler eksiksiz ve hatasız olarak anılmamalıdır. Burada yer alan inner product spaces kelimesi ile ilgili tüm açıklamalar bilgi amaçlıdır. Eksik ve hatalı çevirileri lütfen bildiriniz.
