NORM OF A TENSOR

NORM OF A TENSOR CAN BE DEFINED IN THE FOLLOWING WAY. ANY TENSOR IS A VECTOR belonging to the PRODUCT VECTOR SPACE OVER THE FIELD OF REAL NUMBERS.assume that it is an INNER PRODUCT SPACE.THE BASIC REQUIREMENT IS THAT THE NORM OF A TENSOR MUST MAP A TENSOR TO A REAL NUMBER AND IT MUST REMAIN INVARIANT UNDER admissible coordinate trasformation.NOW CONSIDER A SECOND RANK TENSORIAL SPACE .let T be a second rank tensor.NOW DEFINE norm of T <T,T>.IF T(ij) are the contravariant components&(ij)T are the covariant components of tensor T then the NORM of T[(ij)T].T(ij);summed over i&j.[sudhakarang@alumni.iitm.ac.in]g.sudhakaran is the author of gr-qc/0106029 in xxx.lanl.gov