If T... is a tensor of rank n, show that T... i/ox is a tensor...

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If T... ¡ is a tensor of rank n, show that T... i/ox is a tensor of rank n + 1 (Cartesian coordinates). Note. In non-Cartesian coordinate systems the coefficients a¡¡ are, in general, functions of the coordinates, and the derivatives the components of a tensor of rank n do not form a tensor except in the special case n = 0. In this case the derivative does yield a covariant vector (tensor of rank 1). If T... ¡ is a tensor of rank n, show that T... i/ox is a tensor of rank n + 1 (Cartesian coordinates). Note. In non-Cartesian coordinate systems the coefficients a¡¡ are, in general, functions of the coordinates, and the derivatives the components of a tensor of rank n do not form a tensor except in the special case n = 0. In this case the derivative does yield a covariant vector (tensor of rank 1).

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let a tensor of order 1 be uj aij ui thin Juj 2x1 Now a... View the full answer