Characteristic Polynomial
Calculating Eigenvalues
Calculating EigenvectorsHow to Examples Exercise
How to:
We haven't yet described how the characteristic polynomial relates to the eigenvalues. As you may have already guessed, the roots of this polynomial are in fact the eigenvalues of our matrix. We can use old-fashioned techniques like the quadratic equation to find our roots, OR, if our characteristic polynomial is in row vector form (as is given by poly(A)), there is a much simpler way to find them:
lambdas = roots(poly(A))
The result here is an N-dimensional column vector whose values are the roots of the polynomial, or in this case, the eigenvalues.
NOTE: the roots function works for any polynomial which we represent as a row vector, not just the characteristic polynomial
Of course, MATLAB does not like to make us type any more than we have to, and there is actually an EVEN SIMPLER way of calculating eigenvectors:
lambdas = eig(A)
Examples:
Exercise: