Cauchy-Schwarz Gap

Problem

Return the non-negative gap in the Cauchy-Schwarz inequality:

gap = ||a||_2 * ||b||_2 - |a . b|

A gap of 0 means the vectors are linearly dependent (parallel).

Hint

The gap is zero exactly when one vector is a scalar multiple of the other.

case 1

in: [[3,4],[6,8]]

expected: 0

case 2

in: [[1,0],[0,1]]

expected: 1

case 3

in: [[1,2],[2,1]]

expected: 1

case 4

in: [[0,0],[1,2]]

expected: 0

Starter codePython

def cauchy_schwarz_gap(a, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor