#!F-adobe-helvetica-medium-r-normal--18* #!N #!N #!Rtall529 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 #!Llists1,dxall530 h Lists #!EL #!N #!F-adobe-times-medium-i-normal--18* #!N
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