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Tensor Algebra

In: The Physical and Mathematical Foundations of the Theory of Relativity

Author

Listed:
  • Antonio Romano

    (Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”)

  • Mario Mango Furnari

    (Consiglio Nazionale delle Ricerche, Istituto di Cibernetica)

Abstract

In this chapter the reader is supposed to be acquainted with the algebraic structure of an n-dimensional abstract vector space $$E_n$$ E n . We here show how to generate many other algebraic structures starting from a vector space. We begin by defining the dual vector space, the contravariant, covariant, and mixed tensors. We then collect all these new entities in the global structure of tensor algebra $$T(E_n)$$ T ( E n ) on $$E_n$$ E n . Finally, the exterior algebra, that is the subalgebra of $$T(E_n)$$ T ( E n ) of skew-symmetric covariant tensors, and its geometric meaning are analyzed.

Suggested Citation

  • Antonio Romano & Mario Mango Furnari, 2026. "Tensor Algebra," Springer Books, in: The Physical and Mathematical Foundations of the Theory of Relativity, edition 0, chapter 1, pages 3-49, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-23179-6_1
    DOI: 10.1007/978-3-032-23179-6_1
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