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  2. Linear equation - Wikipedia

    en.wikipedia.org/wiki/Linear_equation

    In mathematics, a linear equation is an equation that may be put in the form + … + + =, where , …, are the variables (or unknowns), and ,, …, are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions , provided they do not contain any of the variables.

  3. Linear algebra - Wikipedia

    en.wikipedia.org/wiki/Linear_algebra

    In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:

  4. List of mathematical examples - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_examples

    This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...

  5. Linear recurrence with constant coefficients - Wikipedia

    en.wikipedia.org/wiki/Linear_recurrence_with...

    In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.

  6. Multilinear polynomial - Wikipedia

    en.wikipedia.org/wiki/Multilinear_polynomial

    In algebra, a multilinear polynomial [1] is a multivariate polynomial that is linear (meaning affine) in each of its variables separately, but not necessarily simultaneously. It is a polynomial in which no variable occurs to a power of 2 {\displaystyle 2} or higher; that is, each monomial is a constant times a product of distinct variables.

  7. Equation - Wikipedia

    en.wikipedia.org/wiki/Equation

    A linear Diophantine equation is an equation between two sums of monomials of degree zero or one. An example of linear Diophantine equation is ax + by = c where a, b, and c are constants. An exponential Diophantine equation is one for which exponents of the terms of the equation can be unknowns.

  8. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1] [2] For example, {+ = + = + = is a system of three equations in the three variables x, y, z.

  9. Linearity - Wikipedia

    en.wikipedia.org/wiki/Linearity

    In mathematics, the term linear is used in two distinct senses for two different properties: . linearity of a function (or mapping);; linearity of a polynomial.; An example of a linear function is the function defined by () = (,) that maps the real line to a line in the Euclidean plane R 2 that passes through the origin.

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