What type of Eigen value can be obtained using Power Method?

The Power Method is a numerical algorithm used to find the dominant eigenvalue of a matrix. The dominant eigenvalue is the eigenvalue with the largest absolute value. This method is particularly useful when dealing with large matrices where other methods may be computationally expensive.

Here are the steps to find the dominant eigenvalue using the Power Method:

1. Start with an initial guess for the eigenvector. This can be any non-zero vector.

2. Multiply the matrix by the current guess for the eigenvector.

3. Normalize the resulting vector (i.e., scale it so that its length is 1).

4. Repeat steps 2 and 3 until the vector converges (i.e., it doesn't change significantly from one iteration to the next).

The resulting vector is an approximation of the dominant eigenvector, and its corresponding eigenvalue can be found by dividing the dot product of the matrix and the eigenvector by the dot product of the eigenvector with itself.

It's important to note that the Power Method only finds the dominant eigenvalue. If you need to find all the eigenvalues of a matrix, you'll need to use a different method.