Lecturer: K.S. Narain , ICTP

lecture 7

*Characteristic Polynomials,*

- Note that in order to be more specific for this semester several things in chapter one have not been mentioned just like tensor calculation and so on.
- on the other hand some of them was given in tutorial .
- The definition of characteristic polynomials by taking a n*n matrix and imposing nth degree polynomial in $\lambda$ are given.Some examples are also given.
- Defining some subspaces with some special examples have been said.
- Decomposing several vectors as a linear combination of the matrices realized.
- Making some subspaces which consist of generalized eigen vectors with rank less than r used.
- Taking basis for any vector by taking into account generalized eigen vectors has been used.
- We proved that generalized igen vectors from different subspaces are linearly independent(was given in the class).
- We present two examples on how to define degeneracy on a 3*3 Matrix.
- We talked a little bit about hamiltonian theorem.