From Vectors to Tensors

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This textbook, deals with tensors that are treated as vectors, and has a practical orientation. In addition to dealing with the classical topics of tensor books, new tensor concepts are introduced, such as the rotation of tensors, the transposer tensor, the eigentensors, the permutation tensor structure, etc. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. In fact, the computational algebra is formulated in matrix form to facilitate its implementation on computers. For the first time tensor contraction is formulated in terms of matrix operations. A computer package , written in Mathematica, is available through Internet at: http://personales.unican.es/castie/tensors that complements the book. In summary, the book is not a standard book on tensors because of its orientation, the many novel contributions included in it, the careful notation and the stretching-condensing techniques used for most of the transformations used in the book.