Category:Definitions/Linear Forms

This category contains definitions related to Linear Forms.
Related results can be found in Category:Linear Forms.

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 $1$.