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  2. Inner product space - Wikipedia

    en.wikipedia.org/wiki/Inner_product_space

    In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space [1] [2]) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in , .

  3. Riemannian manifold - Wikipedia

    en.wikipedia.org/wiki/Riemannian_manifold

    The requirement that is a positive-definite inner product then says exactly that this matrix-valued function is a symmetric positive-definite matrix at . In terms of the tensor algebra , the Riemannian metric can be written in terms of the dual basis { d x 1 , … , d x n } {\displaystyle \{dx^{1},\ldots ,dx^{n}\}} of the cotangent bundle as

  4. Petersson inner product - Wikipedia

    en.wikipedia.org/wiki/Petersson_inner_product

    The integral is absolutely convergent and the Petersson inner product is a positive definite Hermitian form. For the Hecke operators T n {\displaystyle T_{n}} , and for forms f , g {\displaystyle f,g} of level Γ 0 {\displaystyle \Gamma _{0}} , we have:

  5. Interior product - Wikipedia

    en.wikipedia.org/wiki/Interior_product

    In mathematics, the interior product (also known as interior derivative, interior multiplication, inner multiplication, inner derivative, insertion operator, or inner derivation) is a degree −1 (anti)derivation on the exterior algebra of differential forms on a smooth manifold.

  6. Indefinite inner product space - Wikipedia

    en.wikipedia.org/wiki/Indefinite_inner_product_space

    Krein spaces arise naturally in situations where the indefinite inner product has an analytically useful property (such as Lorentz invariance) which the Hilbert inner product lacks. It is also common for one of the two inner products, usually the indefinite one, to be globally defined on a manifold and the other to be coordinate-dependent and ...

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    A man has been arrested after the "serious incident".

  8. Barron Trump Is a 'Ladies Man' at New York University ... - AOL

    www.aol.com/lifestyle/barron-trump-ladies-man...

    Barron Trump is not having trouble fitting in at college.. The 18-year-old son of Donald and Melania Trump has been "popular with the ladies" since starting classes at New York University's Stern ...

  9. Refinance rates for Friday , December 6, 2024 - AOL

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    Rates on a 15-year mortgage stand at an average 6.10% for purchase and 6.13% for refinance, down 8 basis points from 6.18% for purchase and 9 basis points from 6.22% for refinance over the past week.