Mathematical Methods Lecture 5 of 34

September 21, 2011 by K.S. Narain

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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