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

To determine the type of eigenvalue that can be obtained using the Power Method, let’s break down the options provided:

1. Understanding the Power Method: The Power Method is an iterative algorithm used to find the dominant eigenvalue (the eigenvalue with the largest magnitude) of a matrix. It involves multiplying a matrix by an initial vector repeatedly and normalizing it at each step.

2. Evaluating the Choices:

   • a) Largest Eigenvalue: This is indeed the essence of the Power Method. It converges to the largest eigenvalue when applied to a matrix.
   • b) Smallest Eigenvalue: The Power Method does not converge to the smallest eigenvalue; other methods like the Inverse Power Method are better suited for this.
   • c) Largest Eigenvector: The Power Method finds the largest eigenvalue and performs normalization to obtain the corresponding eigenvector, but it does not seek to find the largest eigenvector as a separate concept—rather, it finds the eigenvector associated with the largest eigenvalue.

Conclusion

Given this analysis, the correct answer to the question is:

Final Answer

a) Largest Eigenvalue.