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  2. Stewart's theorem - Wikipedia

    en.wikipedia.org/wiki/Stewart's_theorem

    Diagram of Stewart's theorem. Let a, b, c be the lengths of the sides of a triangle. Let d be the length of a cevian to the side of length a.If the cevian divides the side of length a into two segments of length m and n, with m adjacent to c and n adjacent to b, then Stewart's theorem states that + = (+).

  3. Cevian - Wikipedia

    en.wikipedia.org/wiki/Cevian

    Stewart's theorem. The length of a cevian can be determined by Stewart's theorem: in the diagram, the cevian length d is given by the formula

  4. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

  5. Proof assistant - Wikipedia

    en.wikipedia.org/wiki/Proof_assistant

    In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration. This involves some sort of interactive proof editor, or other interface , with which a human can guide the search for proofs, the details of which are ...

  6. Hermite interpolation - Wikipedia

    en.wikipedia.org/wiki/Hermite_interpolation

    In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation.Lagrange interpolation allows computing a polynomial of degree less than n that takes the same value at n given points as a given function.

  7. Bartels–Stewart algorithm - Wikipedia

    en.wikipedia.org/wiki/Bartels–Stewart_algorithm

    Developed by R.H. Bartels and G.W. Stewart in 1971, [1] it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\displaystyle A} and B {\displaystyle B} to transform A X − X B = C {\displaystyle AX-XB=C} into a triangular system ...

  8. Determinacy - Wikipedia

    en.wikipedia.org/wiki/Determinacy

    The second periodicity theorem implies that, for every natural number n, if Δ 1 2n+1 determinacy holds, then Π 1 2n+1 and Σ 1 2n have the scale property. [7] In particular, if projective determinacy holds, then every projective relation has a projective uniformization .

  9. Cholesky decomposition - Wikipedia

    en.wikipedia.org/wiki/Cholesky_decomposition

    In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.