3 ms·
My favorite kind of pedantry is pedantry that's naive - on like day 1 of topology 101 you learn that the "dot" product is an inner product and every inner produ
by mathisfun123 3y ago
My favorite kind of pedantry is pedantry that's naive - on like day 1 of topology 101 you learn that the "dot" product is an inner product and every inner product naturally induces a metric so every inner product space is a metric space (with the induced metric).
- cochne 3y agoIt’s not pedantry. Just because an inner product induced a metric space does it make it the same thing as that metric. The performance of similarity searches can depend very much on whether you use a dot product or a distance.
- sfpotter 3y agoA distance is a function d(x, y) where d(x, y) = 0 if x = y, if x = 0, or if y = 0 (among other properties). If x = y and neither x = 0 nor y = 0, and if we let d(x, y) = x*y, then d(x, y) != 0 in general, so the dot product is certainly not a distance. Your comment isn't relevant, but thanks for calling me a pedant. ;-)
- mathisfun123 3y ago`is != induces`