Power Iteration

Estimate the dominant eigenvector of a symmetric matrix with power iteration: repeatedly multiply a vector by the matrix and renormalize it.

Implement solve(A, steps=100).

Returns. Return a unit-length NumPy vector after steps iterations (default 100), starting from the all-ones vector. If an iterate becomes the zero vector (for example for the zero matrix) it is returned as is. The overall sign depends on the starting vector.

Examples

Example 1

Input:

solve([[2.0, 0.0], [0.0, 1.0]])

Output:

[1.0, 0.0]

Example 2

Input:

solve([[2.0, 1.0], [1.0, 2.0]])

Output:

[0.707107, 0.707107]