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.