Pseudoinverse of Outer Product

Problem

Compute the Moore-Penrose pseudoinverse of the rank-1 outer product A = a*b^T, where a has length m and b has length n.

Using the formula inv(A^T A) A^T, the pseudoinverse reduces to the n x m matrix (b*a^T) / (||a||^2 * ||b||^2). Return an n x m zero matrix if a or b is the zero vector.

Hint

For a rank-1 matrix, the pseudoinverse is another scaled outer product.

Test cases

case 1

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

expected: [[0.5,0],[0.5,0]]

case 2

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

expected: [[0.5,0],[0,0]]

case 3

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

expected: [[0.25,0.25],[0.25,0.25]]

case 4

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

expected: [[0,0],[0,0]]

Starter codePython

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

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