Relative Perturbation Theory: Iv Sin 2 Theorems 1 Relative Perturbation Theory: Iv Sin 2 Theorems

  title={Relative Perturbation Theory: Iv Sin 2 Theorems 1 Relative Perturbation Theory: Iv Sin 2 Theorems},
  author={Ren-Cang Li},
The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A ! e A = A+A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A ! e A = D AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or e A, in contrast to the gaps that appear in the single angle bounds. The double angle theorems do not directly… CONTINUE READING


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