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From Vectors to Tensors [electronic resource] /by Juan Ramón Ruíz-Tolosa, Enrique Castillo.

by Ruíz-Tolosa, Juan Ramón [author.]; Castillo, Enrique [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Universitext: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: XVI, 670 p. online resource.ISBN: 9783540270669.Subject(s): Mathematics | Matrix theory | Mathematical physics | Engineering mathematics | Mathematics | Linear and Multilinear Algebras, Matrix Theory | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of EngineeringDDC classification: 512.5 Online resources: Click here to access online
Contents:
Basic Tensor Algebra -- Tensor Spaces -- 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.
In: Springer eBooksSummary: 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.
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Basic Tensor Algebra -- Tensor Spaces -- 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.

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.

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