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2 results

  • 7 - Determinant Theory

  • John Stillwell, University of San Francisco
  • Book:
    Algebraic Number Theory for Beginners
    Published online:
    28 July 2022
    Print publication:
    11 August 2022, pp 149-170

  • Summary

    In algebraic number theory the determinant plays a bigger role than in a typical undergraduate linear algebra course. In particular, its relationship to trace, norm, and characteristic polynomial is important. For this reason, we develop determinant theory from scratch in this chapter, using an axiomatic characterization of determinant due to Artin. Among other things, this quickly gives basis-independence of the characteristic polynomial, trace, and norm. With these foundations we can introduce the discriminant, which tests whether an n-tuple of vectors form a basis, and paves the way for integral bases studied in the next chapter.

  • The study of gene–environment interactions in psychiatry: limited gains at a substantial cost?

  • S. Zammit, N. Wiles, G. Lewis
  • Journal:
    Psychological Medicine / Volume 40 / Issue 5 / May 2010
    Published online by Cambridge University Press:
    24 September 2009, pp. 711-716
    • Article
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  • There is an ever-increasing body of literature examining gene–environment interactions in psychiatry, reflecting a widespread belief that such studies will aid identification of novel risk factors for disease, increase understanding about underlying pathological mechanisms, and aid identification of high-risk groups for targeted interventions. In this article we discuss to what extent studies of gene–environment interactions are likely to lead to any such benefits in the future.