Friday, 1 December 2017

general relativity - Transformation matrices for basis and coordinate transformation in non-orthonormal coordinates


The transformation matrices for covariant and contravariant vectors are different but in orthonormal coordinate system numerical values in matrices turn out to be same although in mathematical proof they are related by the operation of transpose of inverse of one of the matrix.





  1. I wanna know how in any non-orthogonal coordinate system these two transformation matrices won't be same?




  2. Also how are they same in any orthonormal coordinate system except Cartesian type coordinate system?






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