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  2. 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]

  3. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    As a result, the method of Lagrange multipliers is widely used to solve challenging constrained optimization problems. Further, the method of Lagrange multipliers is generalized by the Karush–Kuhn–Tucker conditions , which can also take into account inequality constraints of the form h ( x ) ≤ c {\displaystyle h(\mathbf {x} )\leq c} for a ...

  4. Eigenvalue algorithm - Wikipedia

    en.wikipedia.org/wiki/Eigenvalue_algorithm

    Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...

  5. Eigenvalues and eigenvectors - Wikipedia

    en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

    Matrix A acts by stretching the vector x, not changing its direction, so x is an eigenvector of A. Consider n -dimensional vectors that are formed as a list of n scalars, such as the three-dimensional vectors x = [ 1 − 3 4 ] and y = [ − 20 60 − 80 ] . {\displaystyle \mathbf {x} ={\begin{bmatrix}1\\-3\\4\end{bmatrix}}\quad {\mbox{and ...

  6. Exponential integral - Wikipedia

    en.wikipedia.org/wiki/Exponential_integral

    For real non-zero values of x, the exponential integral Ei(x) is defined as ⁡ = =. The Risch algorithm shows that Ei is not an elementary function.The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero.

  7. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗. Similarly, the function has a local minimum point at x ∗, if f(x ∗) ≤ f(x) for all x in X within distance ε of x ∗.

  8. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    In some sources, boldface or double brackets x are used for floor, and reversed brackets x or ]x[for ceiling. [7] [8] The fractional part is the sawtooth function, denoted by {x} for real x and defined by the formula {x} = x − ⌊x⌋ [9] For all x, 0 ≤ {x} < 1. These characters are provided in Unicode:

  9. Maximum satisfiability problem - Wikipedia

    en.wikipedia.org/wiki/Maximum_satisfiability_problem

    MAX-SAT can also be expressed using an integer linear program (ILP). Fix a conjunctive normal form formula F with variables x 1, x 2, ..., x n, and let C denote the clauses of F. For each clause c in C, let S + c and S − c denote the sets of variables which are not negated in c, and those that are negated in c, respectively.