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.