Linear Form

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, ..., x_n is given by the equality

f(x₁, x₂, ⋯, x_n) = a₁x₁ + a₂x₂ + ⋯ + a_nx_n

where a₁, a₂, ..., a_n are constants. If we interpret x₁, x₂, ..., x_n 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.

单词	linear form
释义	Linear Form 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, ..., x_n is given by the equality f(x₁, x₂, ⋯, x_n) = a₁x₁ + a₂x₂ + ⋯ + a_nx_n where a₁, a₂, ..., a_n are constants. If we interpret x₁, x₂, ..., x_n 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.
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