The magnitude of inner product of such functions is relevant to "norm" of the function itself. So when we measure how "line up" two functions exactly, do we divide the inner product by the norm of two functions? (Just like cos<a,b> = a * b / (|a||b|))
Isaaz
Is there any geometric meaning of the inner product?
For vectors the Euclidean inner product is related to angle between them. But for functions I can't imagine what property the inner product is related to.
Or I guess only the Euclidean inner product is nicely picked so it is special.
degrees_K
With the math of both this and the norm, I realized that we are treating the functions as some sort of arrow in infinite dimensions, where each point on the functions is its own dimension, and then integrating instead of simply adding to get a finite result
Heisenberg
Should the functions be normalized before the L2 inner product measures how well they line up?
The magnitude of inner product of such functions is relevant to "norm" of the function itself. So when we measure how "line up" two functions exactly, do we divide the inner product by the norm of two functions? (Just like cos<a,b> = a * b / (|a||b|))
Is there any geometric meaning of the inner product? For vectors the Euclidean inner product is related to angle between them. But for functions I can't imagine what property the inner product is related to. Or I guess only the Euclidean inner product is nicely picked so it is special.
With the math of both this and the norm, I realized that we are treating the functions as some sort of arrow in infinite dimensions, where each point on the functions is its own dimension, and then integrating instead of simply adding to get a finite result
Should the functions be normalized before the L2 inner product measures how well they line up?