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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