What type of Eigen value can be obtained using Power Method?a)Largest Eigen vectorb)Smallest Eigen valuec)Largest Eigen value

Answer

The Power Method is a numerical technique used to find the largest eigenvalue (in absolute value) of a matrix. Here's a brief overview:

1. How the Power Method Works: The Power Method involves iteratively multiplying a vector by the matrix in question. Initially, any non-zero vector is chosen, which eventually converges to the eigenvector associated with the largest eigenvalue.

2. Convergence: As the iterations proceed, the effect of smaller eigenvalues diminishes compared to the largest eigenvalue, leading to convergence to the dominant eigenvalue and corresponding eigenvector.

Given the options:

a) Largest Eigen vector - This is incorrect since it’s not a standard term. b) Smallest Eigen value - This is incorrect as the Power Method does not target the smallest eigenvalue. c) Largest Eigen value - This is correct as the Power Method specifically aims to find the largest eigenvalue.

Final Answer

The type of eigenvalue that can be obtained using the Power Method is c) Largest Eigen value.