This textbook deals with tensors that are treated as vectors, and its orientation is practical. In addition to dealing with the classical topics of standard books on tensors, it introduces new tensor concepts, such as the rotation of tensors, the transposer tensor, the eigentensors, the permutation tensor structure. The book bridges a gap between the classical theory of tensors and the possibility of solving tensor problems with a computer. In fact, the computational algebra required 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 complementing the book and written in Mathematica, is available at:
http://personales.unican.es/castie/tensors.

Addressed primarily to students of engineering, applied mathematics and mathematical physics, this unconventional approach to tensors is original for its orientation, its novel concepts, the choice of notation and the stretching-condensing techniques applied to most of the transformations used.

• Basic Tensor Algebra
  • Tensor Spaces
  • Introduction to Tensors
  • Homogeneous Tensors
  • Change-of-basis in Tensor Spaces
  • Homogeneous Tensor Algebra: Tensor Homomorphisms
• Special Tensors
  • Symmetric Homogeneous Tensors: Tensor Algebras
  • Anti-symmetric Homogeneous Tensors, Tensor and Inner
  • Product Algebras
  • Pseudotensors; Modular, Relative or Weighted Tensors
• Exterior Algebras
  • Exterior Algebras: Totally Anti-symmetric Homogeneous Tensor Algebras
  • Mixed Exterior Algebras
• Tensors over Linear Spaces with Inner Product
  • Euclidean Homogeneous Tensors
  • Modular Tensors over En(IR) Euclidean Spaces
  • Euclidean Exterior Algebra
• Classic Tensors in Geometry and Mechanics
  • Affine Tensors