Outer product, Inner product

Outer product

• uvT
• output: matrix
• time complexity: O(n2)

Inner product

• uTv
• output: scalar
• time complexity: O(n)
  • a = [a0, a1, a2, ... , aN-1], b = [b0, b1, b2, ...., bN-1]
  • a0*b0 + a1*b1 + aN-1*bN-1
  • Assuming that multiplication and addition are constant-time operations, the time-complexity is O(n)
    • Multiply O(n) + add O(n) = O(n)

Top: Inner product, Down: Outer product