Power Iteration Deflation Step

Problem

Deflate the known eigenpair (lam, v) from matrix A, where v is a unit eigenvector:

A' = A - lam * v*v^T

The largest eigenvalue of A' is then the second eigenvalue of A. Return the deflated matrix.

Hint

Subtract the rank-1 spectral component lam*v*v^T.

case 1

in: [[[2,0],[0,3]],2,[1,0]]

expected: [[0,0],[0,3]]

case 2

in: [[[2,1],[1,2]],3,[0.7071067811865475,0.7071067811865475]]

expected: [[0.5,-0.5],[-0.5,0.5]]

case 3

in: [[[4,1],[2,3]],5,[0.7071067811865475,0.7071067811865475]]

expected: [[1.5,-1.5],[-0.5,0.5]]

case 4

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

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

Starter codePython

def deflation_step(A, lam, v):
    # Your code here
    pass

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