Mathematical Methods Lecture 6 of 34

September 23, 2011 by K.S. Narain

K.S. Narain , ICTP

lecture 6

Proving orthonormality using hermition operators, Map beween two subspace, Transformations for Matrices

  • We discuss any vector can be written in terms of linear combination of eigen vectors.
  • Eigen vectors can form basis so hermitian operator can be diagonalized .
  • We proved that statement which was so long and gave some examples.
  • Characteristic Polynomials are given .
  • Decomposition of full vector space in terms of subspace is given.
  • We proved subspace (S_i) consist of generalized eigen vectors of
  • $ A_i$ with eigen value of $\lambda_i$ . Mentioned how many null
  • vectors must be existed in subspaces.
  • ยทDegeneracy of eigen vector with rank 1 is given.
  • Transformations for the explicit Matrices for making them diagonal is expressed.

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