Dot product of vector function?

[lewis198]

Greetings.

I was thinking about finding the angle between two functions, so I thought it may be elegant to turn them into vector valued functions, and find the dot product at a given variable value where the vectors lie on the same plane and are functions of the same variable. I'm going to go away and try it, but what do you guys think about this?

What are the limitations of this method, and/or the advantages?
Thanks guys.

 

[HallsofIvy]

What do you mean by "the angle between two functions"? Do you mean the angle between the tangent lines to their graphs at a point of intersection?

 

[wofsy]

Greetings.

I was thinking about finding the angle between two functions, so I thought it may be elegant to turn them into vector valued functions, and find the dot product at a given variable value where the vectors lie on the same plane and are functions of the same variable. I'm going to go away and try it, but what do you guys think about this?

What are the limitations of this method, and/or the advantages?
Thanks guys.

the angle between two functions is well defined if the functions are square integrable.

you can think of a vector as a function on a finite set so there is really no conceptual difference between a function and a vector.