In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + … + a n x n + b = 0 , {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0...

In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written...

In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example...

regardless of whether known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown...

In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...

interest. A linear Diophantine equation equates the sum of two or more unknowns, with coefficients, to a constant. An exponential Diophantine equation is one...

(see System of polynomial equations). A system of linear equations (or linear system) is a collection of linear equations involving one or more variables...

(If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by...

differential equations (SDEs) where the progression is random. A linear differential equation is a differential equation that is defined by a linear polynomial...

Linear actuator Linear element Linear foot Linear system Linear programming Linear differential equation Bilinear Multilinear Linear motor Linear interpolation...

more than one independent variable. Linear differential equations are the differential equations that are linear in the unknown function and its derivatives...

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

include inverting the matrix of the normal equations and orthogonal decomposition methods. Consider the linear equation where A ∈ R m × n {\displaystyle A\in...

solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by...

Simple equations can be balanced by inspection, that is, by trial and error. Another technique involves solving a system of linear equations. Balanced...

associated plot of the equations. For other ways to solve this kind of equations, see below, System of linear equations. A quadratic equation is one which includes...

q_{0}(x)=0} the equation reduces to a Bernoulli equation, while if q 2 ( x ) = 0 {\displaystyle q_{2}(x)=0} the equation becomes a first order linear ordinary...

single equations, namely as a: System of linear equations, System of nonlinear equations, System of bilinear equations, System of polynomial equations, System...

a single linear equation typically describes a plane and a line is what is common to two distinct intersecting planes. Parametric equations are also used...

waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state...

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...

linear equations in conjunction with known plaintext-ciphertext pairs to derive key bits. For the purposes of linear cryptanalysis, a linear equation...

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves...

proportional to the change in the input. Linear functions are related to linear equations. A linear function is a polynomial function in which the variable x has...

A\mathbf {x} =\mathbf {0} \right\}.} The matrix equation is equivalent to a homogeneous system of linear equations: A x = 0 ⇔ a 11 x 1 + a 12 x 2 + ⋯ + a 1 n...

algorithm is a quantum algorithm for numerically solving a system of linear equations, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd. The algorithm...

analysis. Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum...

methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them...

algebra, linear equations and systems of linear equations over a field are widely studied. "Over a field" means that the coefficients of the equations and...

unknowns or auxiliary variables. This is always possible when all the equations are linear. Such infinite solution sets can naturally be interpreted as geometric...