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Tensors are generalizations of vectors. These manifestate as 1. * product of vector spaces 2. * product of linear maps 3. * multi-indexed arrangements of numbers or scalar functions In the first case we take two vector spaces , and construct a new one by mean of their basis: if V has as basic vectors and W has then is the vector space generated by the symbols which are all the linear combinations of pairs . In another hand, if we want to construct a bilinear map then we pick up a pair of covectors and then we manufacture defined via

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  • Tensor
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  • Tensors are generalizations of vectors. These manifestate as 1. * product of vector spaces 2. * product of linear maps 3. * multi-indexed arrangements of numbers or scalar functions In the first case we take two vector spaces , and construct a new one by mean of their basis: if V has as basic vectors and W has then is the vector space generated by the symbols which are all the linear combinations of pairs . In another hand, if we want to construct a bilinear map then we pick up a pair of covectors and then we manufacture defined via
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abstract
  • Tensors are generalizations of vectors. These manifestate as 1. * product of vector spaces 2. * product of linear maps 3. * multi-indexed arrangements of numbers or scalar functions In the first case we take two vector spaces , and construct a new one by mean of their basis: if V has as basic vectors and W has then is the vector space generated by the symbols which are all the linear combinations of pairs . In another hand, if we want to construct a bilinear map then we pick up a pair of covectors and then we manufacture defined via It is also know that for finite dimensional vector spaces the tensor of rank one are the elements of and its dual space In the multi-indexed versions tensors are expressions like , , , which actualy are the components of tensors and are in nature scalars or scalar functions. In the multi-indexed version tensor are arrays of quantities that obeys certain rules of transformations when we change systems of coordinates.
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