Definition:Homogeneous Expression

This page is about Homogeneous Expression. For other uses, see Homogeneous.

Definition

A homogeneous expression is an algebraic expression in which the variables can be replaced throughout by the product of that variable with a given non-zero constant, and the constant can be extracted as a factor of the resulting expression.

Examples

Arbitrary Example $1$

The polynomial:

$\map E {x, y} = x^2 \map \sin {x / y} + y^2 \map \cos {x / y}$

is a homogeneous expression.

Also see

• Results about homogeneous expressions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): homogeneous
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): homogeneous