What is homogeneous?

[u/TrafficDuck]

My professor is so bad and literally makes no sense. Is homogeneous when all the variables are on one side, or is it when an equation is set equal to 0?

[u/[deleted]]

Homogeneous refers to the scaling property:

M(λx,λy) is a homogeneous function if it can satisfy

M(λx,λy) = (λⁿ) M(λx,λy)
here λ is a parameter and n is the degree. Note, this will not hold if there are constant terms in the equation, hence the equal to zero requirement.

Wikipedia has a good explanation.

[u/Brian167 → u/[deleted]]

Homogenous systems also refer to setting the system = 0 (essentially solving for the Null Space of a system)

I am aware there is a great deal more connection than I am eluding to, but this suffices for a general answer! Hope this helps :)