Definition:Linear Form

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Linear Form may refer to:

Linear Form (Linear Algebra)

Let $\struct {R, +, \times}$ be a commutative ring.

Let $\struct {R, +_R, \circ}_R$ denote the $R$-module $R$.

Let $\struct {G, +_G, \circ}_R$ be a module over $R$.


Let $\phi: \struct {G, +_G, \circ}_R \to \struct {R, +_R, \circ}_R$ be a linear transformation from $G$ to the $R$-module $R$.


$\phi$ is called a linear form on $G$.


Linear Form (Polynomial Theory)

A linear form is a form whose variables are of degree $1$.