Class 8



  1. L-invariant subspaces and L-cyclic subspace generated by v in V continued. In particular, we went over the example on page 31 of the class notes. We saw that the L-cyclic subspace was L-invariant and dimension 3 (in R^4), for the given v=[0 0 1 1]. We then tried v=[1 1 1 1] and also got dimension 3. However, this was only a coincidence, as can be seen by using the vector v=[0 0 1 0] or some random vector. A matlab file with its output is available to see this. However, we will see that properties of the minimum polynomial will help us obtain L-cyclic subspaces of small dimension, e.g. see the matlab file with its output.