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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. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    It is often called the inner product (or rarely the projection product) of Euclidean space, even though it is not the only inner product that can be defined on Euclidean space (see Inner product space for more). Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers.

  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. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    The inner product is an example of a bilinear form, and it gives the vector space a geometric structure by allowing for the definition of length and angles. Formally, an inner product is a map ⋅ , ⋅ : V × V → F {\displaystyle \langle \cdot ,\cdot \rangle :V\times V\to F}

  7. First fundamental form - Wikipedia

    en.wikipedia.org/wiki/First_fundamental_form

    In differential geometry, the first fundamental form is the inner product on the tangent space of a surface in three-dimensional Euclidean space which is induced canonically from the dot product of R 3. It permits the calculation of curvature and metric properties of a surface such as length and area in a manner consistent with the ambient space.

  8. This practice in the health insurance industry may have ... - AOL

    www.aol.com/finance/practice-health-insurance...

    This practice in the health insurance industry may have ‘gotten out of control,’ Wall Street analyst says

  9. Cauchy–Schwarz inequality - Wikipedia

    en.wikipedia.org/wiki/Cauchy–Schwarz_inequality

    where , is the inner product.Examples of inner products include the real and complex dot product; see the examples in inner product.Every inner product gives rise to a Euclidean norm, called the canonical or induced norm, where the norm of a vector is denoted and defined by ‖ ‖:= , , where , is always a non-negative real number (even if the inner product is complex-valued).