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Tensors #!N #!N #!N Tensors are a generalization of the concept 
of vectors. On one hand, the elements in a tensor have 
meanings that are independent of the coordinate system in which they 
are embedded. On the other hand, one can associate certain metrics 
to them that vary among coordinate systems. #!N #!N In general, 
a rank  #!F-adobe-times-medium-i-normal--18*   n #!EF tensor can be formed by surrounding 
 #!F-adobe-times-medium-i-normal--18*   k #!EF rank  #!F-adobe-times-medium-i-normal--18*   n #!EF -1 tensors with square 
brackets. (Note that scalars, vectors, and matrices are rank 0, 1, 
and 2 tensors, respectively.) As with the matrices, all of the 
subtensors must have the same shape. #!N #!N The following are 
valid tensors: #!N #!N #!CForestGreen #!N  #!F-adobe-courier-bold-r-normal--18*   #!N [[[[[0xabcd]]]]] // a 
1x1x1x1x1 rank 5 tensor #!N #!N [[[1 0 0] // a 
3x3x3 rank 3 tensor with #!N [0 0 0] // 1's 
on the diagonal #!N [0 0 0]] #!N [[0 0 0] 
#!N [0 1 0] #!N [0 0 0]] #!N [[0 0 
0] #!N [0 0 0] #!N [0 0 1]]] #!EF #!N 
#!N #!EC #!N #!N #!N  #!F-adobe-times-medium-i-normal--18*   Next Topic #!EF #!N #!N 
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