Question on generalized eigenspaces

Hi Sir,

I’ve completed the computation of the first part of question 3. However I don’t understand how to find the basis for each generalized eigenspace. Couldyou direct me to which area of the notes that I sould read up on or give me an example please.

Thanks

Reply:

Finding a basis for generalized eigenspaces is simply the old problem of finding a basis for the solution space of a system of equations. That is, given a linear map

L:V-> V

the t-th generalized eigenspace V_t(a) for some eigenvalue a is simply the set of solutions v to

[(L-aI)^t]v=0

For any specific L in matrix form and specific eigenvalue a, (L-aI)^t will again be a matrix, and you are asked to find a basis for the solution space to the linear system above. I’m sure you know how to do it. Look also at example 3.4.61 in the notes.

If you still can’t do it, try asking again.

MK

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