Mathematical Methods Lecture 4 of 34

September 19, 2011 by K.S. Narain

K.S. Narain , ICTP

Linear operators and finite dimensional vector space with n dimension

  • Any finite vector space can be presented by linear operator with N*N matrix.
  • Finite dimensional space and giving several examples for those matrices.
  • Power series expansion and some application are given.
  • Identity operator and its properties and the prove for existing of Inverse matrix are mentioned
  • The definition of adjoint operator and some of its properties have been said.
  • Hermitian operator ,Projection operator , the definition of eigen value and eigen vectors are given.
  • The prove of rank one for vectors is included .Ordinary eigenvector is also introduced.
  • Generalized ordinary vector is expressed.

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