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2 results

  • 2 - Introduction to Matrices

  • Jeffrey A. Fessler, University of Michigan, Ann Arbor, Raj Rao Nadakuditi, University of Michigan, Ann Arbor
  • Book:
    Linear Algebra for Data Science, Machine Learning, and Signal Processing
    Published online:
    01 November 2024
    Print publication:
    16 May 2024, pp 12-62

  • Summary

    This chapter reviews vectors and matrices, and basic properties like shape, orthogonality, determinant, eigenvalues, and trace. It also reviews operations like multiplication and transpose. These operations are used throughout the book and are pervasive in the literature. In short, arranging data into vectors and matrices allows one to apply powerful data analysis techniques over a wide spectrum of applications. Throughout, this chapter (and book) illustrates how the ideas are implemented in practice in Julia.

  • Stabilized automorphism group of odometers and of Toeplitz subshifts

  • Part of
  • JENNIFER N. JONES-BARO
  • Journal:
    Ergodic Theory and Dynamical Systems / Volume 44 / Issue 8 / August 2024
    Published online by Cambridge University Press:
    13 November 2023, pp. 2289-2307
    Print publication:
    August 2024
    • Article
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  • We characterize the stabilized automorphism group for odometers and Toeplitz subshifts, and then prove an invariance property of the stabilized automorphism group of these dynamical systems. Namely, we prove the isomorphism invariance of the primes for which the p-adic valuation of the period structure tends to infinity. A particular case of interest is that for torsion-free odometers, the stabilized automorphism group is a full isomorphism invariant.