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We investigate the condition number for a complex eigenvalue of a real matrix under real perturbations. Based on an explicit formula, it is shown that this number is never smaller than 1/root2 times the corresponding condition number with respect to comple ...
We report the growth of highly reflective distributed Bragg reflectors (DBRs) in the UV region using the Al0.85In0.15N/Al0.2Ga0.8N lattice-matched system. The DBRs were deposited on nearly strain-free Al0.2Ga0.8N templates to avoid strain-induced structura ...
Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive rth root of unity, one obtains under certain conditions a normal basis for mathbbFqn over Fq, where r is a prime and ...
A corollary of the main theorem presented in this note is a generalisation of the well-known result that a self-adjoint square root of a positive self-adjoint compact linear map in a Hilbert space is itself a compact linear map. The method used here exploi ...
