homogeneous function
A "homogeneous function" is a mathematical function that exhibits specific scaling properties, often used in calculus, algebra, and differential equations.
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Definition
C2Mathematics
(technical, academic)A function that scales in a specific way when all its inputs are multiplied by a constant, resulting in the function being multiplied by a power of that constant.
Example
- The function f(x, y) = x^2 + y^2 is homogeneous of degree 2 because scaling both x and y by a constant k scales the function by k^2.
- Homogeneous functions are often used to solve differential equations where variables can be separated by scaling.
C2Algebra
(technical, academic)A polynomial function where all terms have the same degree.
Example
- The polynomial 3x^3 + 2x^2y + y^3 is not a homogeneous function because the terms have different degrees.
- In algebra, homogeneous functions help simplify the study of polynomial equations.
Similar
Terms that have similar or relatively close meanings to "homogeneous function":