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Translations for „inner product“ in the English » Arabic Dictionary

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inner product MATH

Monolingual examples (not verified by PONS Editors)

English
Any complete inner product space has an orthonormal basis.
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The inner product is a generalization of the dot product of vectors.
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The corresponding quadratic form is a multiple of the standard inner product.
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Orthonormal bases are convenient to work with because the inner product of two vectors have simple expressions.
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This definition of orthonormal basis generalizes to the case of infinite-dimensional inner product spaces in the following way.
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The spectral theorem provides a canonical form for symmetric, unitary and more generally normal operators on finite dimensional inner product spaces.
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The derivation property follows by this and the associativity property of the inner product in the identity above.
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