Linear equation

The linear equation (it presents Kei not to work as and comes linear equation) is an equation expressed by an equation of the representation (function, operator) with the linear nature. I refer to a linear gender for the character, shaking such as the linear shape for written on the cover.

Stack alignment of the solution is managed from the linear nature, and, in the linear equation, many good properties are managed. The technique such as lines was arranged by the study of the linear equation (particularly multivariate primary algebraic equation), and a field was formed for one minute called the linear algebra.

A result applicable widely is known saying that I took a linear equation coefficient out of the meeting that addition, subtraction, multiplication and division operation can release not only a real number and complex number (in other words, I have the algebraic structure called the body) in the case of most by linear algebraic maintenance.

I assume following particularly meeting K which takes a coefficient when I do not decline it a body (commutation). In many cases, I think that K is meeting C to form of meeting R which the whole real number makes or the whole complex number and do not interfere.

• Linear equation: Equation a(x) = b about unknown x when linear representation a and fixed number b are given
• Linear differential equation: Linear representation a and differential calculus ∂ x: = Define differential operator a (∂ x) for d/dx; and a (think about ∂ x)y = b.
• 線型漸化式, linear dynamics system

Principle of superposition

If X, Y is the solution of the equation, after all, from the linear nature to have of 斉次方程式, linear combination αX +βY becomes the solution of the equation, too. It is said that principle of superposition is managed referring to this. If a special solution having one equation that is not 斉次 is found, other solutions are provided by adding a solution of 斉次方程式 belonging to the equation.

Therefore, the whole of the solution of the linear equation makes one vector space (or アフィン space). This is called the solution space of the equation.

Allied item

• Linear problem

Outside link

• linear equation - PlanetMath.

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