Question

How do I get eigenvectors and eigenvalues out of a matrix?

Answer 1

This actually a bit difficult for an explanation in here,but you could use GOOGLE and khan-academy to learn about it.

Answer 2

I must learn it in order to understand the material in the AI class.

Answer 3

you need to create the characteristic equation first:
\[\det (A-\lambda I)=0\] if the matrix A is an n x n matrix, this will be a degree n polynomial whose solutions are the eigenvalues.

Once you have these values, you need to find a basis for the kernel (or Null Space) of the matrix:\[A-\lambda_i I\]for each eigenvalue. The basis will be the eigenvectors.