We are what we think we are!

Abstract

Recall that, for two vectors x = (x1, x2, . . . , xn) and y = (y1, y2, . . . , yn) in R n , their dot product x · y is defined as x1y1 + x2y2 + · · · + xnyn. Here, n ≥ 1 is a natural number. Note that when n = 1, this dot product is just the product of the two real numbers x and y. Consider the Euclidean space E n := (R n , ·), that is, our usual finite dimensional vector space R n equipped with the dot product.