Characteristic Polynomial
Calculating Eigenvalues
Calculating EigenvectorsHow to Examples Exercise
How to:
There are many applications to finding the eigenvalues of an NxN matrix. Eigenvalues are simply scalar multiples, denoted as lambda, that satisfy the equation:
A*v = lambda*v
An important tool in finding these eigenvalues is the characteristic polynomial. The characteristic polynomial is found using the equation:
det(lambda*eye(n) - A)
Or in other words the determinant of lambda times the identity matrix minus A.
MATLAB provides us with a much simpler way for finding the characteristic polynomial:
CP = poly(A)
This function results in an N+1-dimensional row vector whose entries are the coefficients of our characteristic polynomial. That is:
CP(1, 1)*lambda^n + CP(1, 2)*lambda^(n-1) + ... + CP(1, n)*lambda + CP(1, n+1)
Examples:
Exercise: