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Tensor and matrix

  1. Dec 20, 2015 #1
    Each set of constant numbers such as ##(v_1, v_2, v_3)## are the components of a constant Cartesian vector because by rotation of coordinates they satisfy the transformation rule. Can we consider each set of constant arrays ## a_{ij};i,j=1,2,3 ## as components of a Cartesian tensor? In other words, does each set of this type satisfy the tensor transformation rule?
  2. jcsd
  3. Dec 20, 2015 #2


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    What do you mean by a Cartesian tensor? Cartesian is usually used to refer to a coordinate system, not a tensor, or a vector, both of which are coordinate-independent objects.
    Given any 3 x 3 Cartesian coordinate system, the matrix you mention will be the representation in that coordinate system of a tensor.
  4. Dec 21, 2015 #3
    Thanks. By "Cartesian tensor" I meant the representation of a tensor in Cartesian coordinate system.
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