Orthogonal Iteration Step

Problem

Perform one step of orthogonal iteration (subspace iteration) on A with orthogonal matrix Q:

Compute Z = A*Q, then orthonormalize the columns of Z with Gram-Schmidt and return the new orthogonal matrix Q_new.

Hint

Repeated orthogonal iteration converges to the dominant invariant subspace.

case 1

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

expected: [[1,0],[0,1]]

case 2

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

expected: [[1,0],[0,1]]

case 3

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

expected: [[1,0],[0,1]]

case 4

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

expected: [[0,1],[1,0]]

Starter codePython

def orthogonal_iteration_step(A, Q):
    # Your code here
    pass

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