Mark Johnson: A brief introduction to kernel classifiers

http://cs.brown.edu/courses/cs195-5/fall2009/docs/lecture_10-27.pdf

Question:

Let's have two vectors
a=(a1,a2,a3)
b=(b1,b2,b3)
and a function K: (R^3,R^3) ⇒ R,
K(a,b) = (a*b)^2 = (a1*b1 + a2*b2 + a3*b3)^2
Can you define function h: R^3 ⇒ R^m
such that h(a) * h(b) = K(a,b)?

Hint:
See slide 10 for inspiration.