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2 results

  • 12 - Elasticity

  • Dimitrios Kolymbas, University of Innsbruck
  • Book:
    A Primer on Theoretical Soil Mechanics
    Published online:
    14 July 2022
    Print publication:
    04 August 2022, pp 88-91

  • Summary

    The general definition of elasticity is given, and as a special case the linear elasticity with Hooke’s law, is presented together with its derivation on the basis of the Cayley–Hamilton theorem. Some applications of elasticity theory in soil mechanics are presented.

  • A lower bound for the degree of polynomials satisfied by matrices

  • Part of
  • K. R. Pearson
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics / Volume 27 / Issue 4 / June 1979
    Published online by Cambridge University Press:
    09 April 2009, pp. 430-436
    Print publication:
    June 1979
    • Article
      • You have access
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  • R. Paré and W. Schelter (1978) have extended the Cayley-Hamilton theorem by showing that for each n<1 there is an integer k such that all n x n matrices over any (possibly noncommutative) ring satisfy a monic polynomial of degree k. We give a lower bound for this degree, namely π(n), which is defined as the shortest possible length of a sequence with entries from {1, 2, …, n}.