2 × 2 Matrices That Are Roots of Unity

  • Alexander A. Roytvarf


As readers know, a polynomial equation of degree n has at most n roots (considering multiplicity) in a number field containing its coefficients. How many roots does a polynomial equation have in a matrix ring? First, how many roots of degree n of 1=E, that is, matrices X, \(X^n = {X \circ \ldots \circ X}_n = E\) are there? And how would one enumerate them? These and related questions that can be answered given a relatively modest level of knowledge on the reader’s part are discussed in this chapter. That is, we will characterize the roots of E in a ring of 2×2 matrices with real entries and show some applications to other mathematical topics: matrix norm estimation and spectral analysis of 3-diagonal Jacobi matrices.


Linear Operator Problem Group Normed Vector Space Jordan Canonical Form Trigonometric Identity 
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© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  • Alexander A. Roytvarf
    • 1
  1. 1.Rishon LeZionIsrael

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