# Linear Form

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## linear form

[′lin·ē·ər ′fȯrm]
(mathematics)
A homogeneous polynomial of the first degree.

## Linear Form

a form of the first degree. A linear form in n variables x1, x2, ..., xn is given by the equality

f(x1, x2, ⋯, xn) = a1x1 + a2x2 + ⋯ + anxn

where a1, a2, ..., an are constants. If we interpret x1, x2, ..., xn as the coordinates of a vector x in an n-dimensional vector space, then f will satisfy the relation

f(αx + βy) = αf(x) + βf(y)

(where x and y are vectors and α and β are numbers). Conversely, a form satisfying this relation is linear.

References in periodicals archive ?
Dubickas, On the degree of a linear form in conjugates of an algebraic number, Illinois J.
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The linear form of the Temkin isotherm is represented in equation (5):
Nail changes secondary to porokeratosis are less common, and if they occur they are mostly seen in linear form.
The linear form Langmuir isotherm equation can be represented by:
Doctor] intentionally put this document in a linear form, because so many of us think like that," she said.
In this paper we consider a general single-index models with the partial linear form
Correlation between soil organic matter and soil carbon stock presented in linear form with [R.
We have gone for a linear form of prediction equation to make computations easier.
i] are coprimes coefficients of a linear form with p ; bi is the byte of data in binary or decimal system

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