The finiteness conjecture for the generalized spectral radius of a set of matrices

@article{Lagarias1995TheFC,
  title={The finiteness conjecture for the generalized spectral radius of a set of matrices},
  author={J. Lagarias and Y. Wang},
  journal={Linear Algebra and its Applications},
  year={1995},
  volume={214},
  pages={17-42}
}
  • J. Lagarias, Y. Wang
  • Published 1995
  • Mathematics
  • Linear Algebra and its Applications
  • The generalized spectral radius\g9(∑) of a set ∑ of n × n matrices is \g9(∑) = lim supk→∞\g9k(∑)1k, where \g9k(∑) = sup{ϱ(A1A2…Ak): each Ai ∈ ∑}. The joint spectral radius\g9(∑) is \g9(∑) = lim supk→∞\g9k(∑)1k, where \g9k(∑) = sup{∥A1 … Ak∥:each Ai ∈ ∑}. It is known that \g9(∑) = \g9(∑) holds for any finite set ∑ of n × n matrices. The finiteness conjecture asserts that for any finite set ∑ of real n × n matrices there exists a finite k such that \g9(∑) = \g9(∑) = \g9k(∑)1k. The normed… CONTINUE READING
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    References

    SHOWING 1-10 OF 18 REFERENCES
    Stability of discrete linear inclusion
    • 316
    • Highly Influential
    Two-scale difference equations I: existence and global regularity of solutions
    • 396
    Bounded semigroups of matrices
    • 356
    • PDF
    Matrix Perturbation Theory
    • 2,041
    • Highly Influential
    The characterization of continuous, four-coefficient scaling functions and wavelets
    • 54