Mathematical methods Lecture 4 of 34

September 28, 2012 by Multimedia Publications and Printing Services

Lecturer: 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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