Notes

what is homogeneous
In mathematics, homogeneous refers to a property of an equation or function w here all of its terms have the same degree or power. More specifically, a function or equation is said to be homogeneous of degree n if multiplying most of its variables by a constant factor k results in the event or equation being multiplied by k^n.

For example, the event f(x, y) = 2x^2 + 3xy - y^2 is homogeneous of degree 2 because all of its terms have a degree of 2 once the variables are raised to a power.

Homogeneous equations and functions have several important properties in mathematics and physics. For instance, in economics, the production function is frequently assumed to be homogeneous of degree one, which means that increasing all inputs by a constant factor results in a proportional upsurge in output.

In Additional info , homogeneous functions are essential in the study of scaling and self-similarity, where certain physical phenomena exhibit exactly the same behavior at different scales.
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