Thread: inner product space

Hi!
I assume that the space R is given. I have a question about an inner product space. One of the axiom is following: (ax,y)=a(x,y). Why we need this axiom? Exist a function, that don't satisfies this axiom, but satisfies others axioms about inner product space?

Originally Posted by analysis

Hi!
I assume that the space R is given. I have a question about an inner product space. One of the axiom is following: (ax,y)=a(x,y). Why we need this axiom? Exist a function, that don't satisfies this axiom, but satisfies others axioms about inner product space?

Can you restate the question? You want to know why homogeneity (that's the property you're talking about) is important? You want to know if there exists functions which satisfy the other axioms of an inner product except homogenity?

Originally Posted by Drexel28

Can you restate the question? You want to know why homogeneity (that's the property you're talking about) is important? You want to know if there exists functions which satisfy the other axioms of an inner product except homogenity?

Yes, I want to know if there exists functions which satisfy the other axioms except homogenity. I have been thinking about this topic for 2 weeks, and I can't find this special function, therefore I don't understand why do we need this axiom about the homogenity