Mathematical methods Lecture 5 of 34

September 29, 2012 by Multimedia Publications and Printing Services

Lecturer: K.S. Narain , ICTP

Some of the contents in this lecture are not in the book.

The inverse of Matrix, Eigen value equation, Standard matrix multiplication ,Transformation for covariant and contra variant objects   

  • Determinant of 2*2  and 3*3  Matrix introduced.
  • Writing determinant of a matrix in a compact form in terms of
  • Levi Chevita tensor  and its properties and  various examples are given.
  • Determinant of product of two matrices is also explained.
  • Showing n-linear inhomogeneous equation for n-unknown quantities and the prove is given by contradiction.
  • By introducing several examples for adjoint , hermition and unitary operators we learn how to come over those things.
  • The definition of scalar is given .we proved that determinant of matrix will not change under changing of the basis .
  • We prove that the scalars which are invariant just like the trace of a
  •  matrix and we discussed cyclic property of the trace. 
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