Theorem 9.18.
For every n∈Nn∈Nthere is a bijection between Bi(Fn)Bi(Fn)and MFn∩Fix(1)MFn∩Fix(1), where MFnMFnis the phasing manifold of dimension 2n−12n−1.
The above theorem indicates the resilience of Conjecture 1.1. Another approach towards this conjecture has been designed by Gabidulin. Unfortunately, even in the prime case, where some details are provided, he EDC.HCl does not explain how to exclude that Bi(Fn)Bi(Fn) is infinite but countable. Therefore, the only accessible confirmation of the conjecture in the prime case is [35].
10. Numerical results
10.1. A simple algorithm and its properties
In the proof of Theorem 4.1(b) we have shown that ‖A‖∞→1≤n‖A‖∞→1≤n for every A∈U(n). As we pointed out in Remark 4.2, biunimodular vectors for A are precisely those, where the norm ‖A‖∞→1=n‖A‖∞→1=n is attained. Thus, if v is a biunimodular vector of A , then we can think of it as of a point on TnTn, where the norm ‖Av‖1‖Av‖1 is maximized.
For every n∈Nn∈Nthere is a bijection between Bi(Fn)Bi(Fn)and MFn∩Fix(1)MFn∩Fix(1), where MFnMFnis the phasing manifold of dimension 2n−12n−1.
The above theorem indicates the resilience of Conjecture 1.1. Another approach towards this conjecture has been designed by Gabidulin. Unfortunately, even in the prime case, where some details are provided, he EDC.HCl does not explain how to exclude that Bi(Fn)Bi(Fn) is infinite but countable. Therefore, the only accessible confirmation of the conjecture in the prime case is [35].
10. Numerical results
10.1. A simple algorithm and its properties
In the proof of Theorem 4.1(b) we have shown that ‖A‖∞→1≤n‖A‖∞→1≤n for every A∈U(n). As we pointed out in Remark 4.2, biunimodular vectors for A are precisely those, where the norm ‖A‖∞→1=n‖A‖∞→1=n is attained. Thus, if v is a biunimodular vector of A , then we can think of it as of a point on TnTn, where the norm ‖Av‖1‖Av‖1 is maximized.