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Access provided by: anon Sign Out. An Introduction to the Rudiments of Tensor Analysis Abstract: The notion of a tensor is developed in terms presumed familiar to the reader; tensors are shown to be a natural outgrowth and extension of vectors and matrices. The paper begins with an elementary discussion of affine vector spaces in a way which presupposes no prior contact with linear algebra on the part of the reader.

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The notions of the contravariant and covariant components of a vector are introduced early and the vector is characterized as a tensor of rank one so that the reader may readily generalize the results to tensors of higher ranks. Roughly, the discussion is divided into two major headings, Tensor Algebra and Tensor Analysis; a brief introduction to differential geometry where tensor analysis achieves its greatest power and beauty is included under the latter heading.

Article :. Tensors of type form a vector space.

### An introduction to tensor analysis for engineers and applied scientists

This description generalized to any tensor type, and an invertible linear map induces a map , where is the dual vector space and the Jacobian , defined by. This definition can be extended similarly to other tensor products of and. When there is a change of coordinates , then tensors transform similarly, with the Jacobian of the linear transformation.

Portions of this entry contributed by Todd Rowland.

Abraham, R. Manifolds, Tensor Analysis, and Applications, 2nd ed. New York: Springer-Verlag, Akivis, M. An Introduction to Linear Algebra and Tensors. New York: Dover, Arfken, G.

Orlando, FL: Academic Press, pp. Aris, R. Bishop, R. Tensor Analysis on Manifolds. Borisenko, A. Vector and Tensor Analysis with Applications. Bott, R. Differential Forms in Algebraic Topology. The Theory of Spinors. Joshi, A.

## An Introduction to Tensor Calculus & Relativity

Matrices and Tensors in Physics, 3rd ed. Wiley, Lass, H. Vector and Tensor Analysis. New York: McGraw-Hill, Lawden, D. Chichester, England: Wiley, Lovelock, D. Tensors, Differential Forms, and Variational Principles.

McConnell, A. Applications of Tensor Analysis.

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- An Introduction to Tensor Calculus & Relativity.
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Nicolaescu, L. Lectures on the Geometry of Manifolds.

Singapore: World Scientific, Parker, L. Reading, MA: Addison-Wesley, Rashevskii, P.

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## [math/] Quick introduction to tensor analysis

Riemann'sche Geometrie und Tensoranalysis. Berlin: Deutscher Verlag der Wissenschaften, Simmonds, J. A Brief on Tensor Analysis, 2nd ed.