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Linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. [1]

38 relations: Affine space, Algebraic equation, Applied mathematics, Cartesian coordinate system, Coefficient, Complex number, Consistent and inconsistent equations, Constant term, Coordinate system, Determinant, Elementary algebra, Equation, Equation solving, Euclidean space, Extrapolation, Field (mathematics), Gaussian elimination, Graph of a function, Hyperplane, Interpolation, Line (geometry), Linear algebra, Linear belief function, Linear equation over a ring, Linear inequality, Linear map, Mathematics, Nonlinear system, Real number, Scalar (mathematics), Simultaneous equations, Slope, System of linear equations, Tax bracket, Term (logic), Three-dimensional space (mathematics), Variable (mathematics), Vertical line test.

Affine space

In mathematics, an affine space is a geometric structure that generalizes certain properties of parallel lines in Euclidean space.

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Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

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Applied mathematics

Applied mathematics is a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

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Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variables of the expression.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

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Consistent and inconsistent equations

In mathematics and in particular in algebra, a linear or nonlinear system of equations is consistent if there is at least one set of values for the unknowns that satisfies every equation in the system—that is, that when substituted into each of the equations makes the equation hold true as an identity.

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Constant term

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.

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Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space.

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Determinant

In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix.

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Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

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Equation

In mathematics, an equation is an equality containing one or more variables.

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Equation solving

In mathematics, to solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality).

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Extrapolation

In mathematics, extrapolation is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable.

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Field (mathematics)

In abstract algebra, a field is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

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Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

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Graph of a function

In mathematics, the graph of a function f is the collection of all ordered pairs.

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Hyperplane

In geometry a hyperplane is a subspace of one dimension less than its ambient space.

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Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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Linear algebra

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces.

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Linear belief function

Linear Belief Function is an extension of the Dempster-Shafer theory of belief functions to the case when variables of interest are continuous.

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Linear equation over a ring

In algebra, linear equations and systems of linear equations over a field are widely studied.

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Linear inequality

In mathematics a linear inequality is an inequality which involves a linear function.

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Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

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Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

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Nonlinear system

In physics and other sciences, a nonlinear system, in contrast to a linear system, is a system which does not satisfy the superposition principle – meaning that the output of a nonlinear system is not directly proportional to the input.

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Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

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Scalar (mathematics)

In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.

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Simultaneous equations

In mathematics, a set of simultaneous equations, also known as a system of equations, is a finite set of equations for which common solutions are sought.

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Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

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System of linear equations

In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.

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Tax bracket

Tax brackets are the divisions at which tax rates change in a progressive tax system (or an explicitly regressive tax system, although this is much rarer).

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Term (logic)

In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

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Three-dimensional space (mathematics)

Three-dimensional space (also: tri-dimensional space) is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists.

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Variable (mathematics)

In elementary mathematics, a variable is an alphabetic character representing a number, called the value of the variable, which is either arbitrary or not fully specified or unknown.

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Vertical line test

In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not.

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References

[1] https://en.wikipedia.org/wiki/Linear_equation

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