Mathematical Methods Lecture 7 of 34

September 26, 2011 by K.S. Narain


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.

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