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.

Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some "background" state. Linear equations do not include exponents.

Read more about Linear EquationLinear Equations in Two Variables, Linear Equations in More Than Two Variables

Other articles related to "equation, equations, linear equation, linear equations, linear":

First-order Non-singular Perturbation Theory
... in simplified terms, the general theory for the perturbative solution to a differential equation to the first order ... Suppose one wants to solve a differential equation of the form where D is some specific differential operator, and is an eigenvalue ... involving ordinary or partial differential equations can be cast in this form ...
Linear Equations in More Than Two Variables
... A linear equation can involve more than two variables ... The general linear equation in n variables is In this form, a1, a2, …, an are the coefficients, x1, x2, …, xn are the variables, and b is the constant ... Such an equation will represent an (n–1)-dimensional hyperplane in n-dimensional Euclidean space (for example, a plane in 3-space) ...
Line (geometry) - Euclidean Geometry - Coordinate Geometry
... In coordinate geometry, lines in a Cartesian plane can be described algebraically by linear equations ... In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form where m is the slope or gradient of the line ... xa ≠ xb, is given by m = (yb-ya)/(xb-xa) and the equation of this line can be written y = m(x - xa) + ya ...
Linear Cryptanalysis - Overview - Constructing Linear Equations
... For the purposes of linear cryptanalysis, a linear equation expresses the equality of two expressions which consist of binary variables combined with the exclusive-or (XOR) operation ... For example, the following equation, from a hypothetical cipher, states the XOR sum of the first and third plaintext bits (as in a block cipher's block) and the first ciphertext bit is equal to ... Since the equations dealt with in linear cryptanalysis will vary in probability, they are more accurately referred to as linear approximations ...

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    Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.
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