Outline for Eigenstuff problems
Example 1
i) Compute A − λI
ii) Compute det(A − λI). This gives you the characteristic polynomial.
iii) Set the characteristic polynomial equal to zero and find the roots. These are your eigenvalues.
The algebraic multiplicity is the number of times a specific root occurs (e.g. in the problem
you sent to me 2 occurs twice so its algebraic multiplicity is 2).
iv) Using row operations find the rref A − λI for your corresponding eigenvalues. This gives you
your Eigenspaces as well as your eigenvectors
Example 1
i) Compute A − λI
ii) Compute det(A − λI). This gives you the characteristic polynomial.
iii) Set the characteristic polynomial equal to zero and find the roots. These are your eigenvalues.
The algebraic multiplicity is the number of times a specific root occurs (e.g. in the problem
you sent to me 2 occurs twice so its algebraic multiplicity is 2).
iv) Using row operations find the rref A − λI for your corresponding eigenvalues. This gives you
your Eigenspaces as well as your eigenvectors
