کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4602521 1631169 2008 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Defect of a unitary matrix
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Defect of a unitary matrix
چکیده انگلیسی

We analyze properties of a map f sending a unitary matrix U of size N into a doubly stochastic matrix B = f(U) defined by Bi,j = ∣Ui,j∣2. For any U we define its defect, determined by the dimension of the image Df(TUU) of the space TUU tangent to the manifold of unitary matrices U at U under the tangent map Df corresponding to f. The defect of U equal to zero for a generic unitary matrix, gives an upper bound for the dimension of a smooth orbit (a manifold) stemming from U of inequivalent unitary matrices mapped into the same doubly stochastic matrix B = f(U). We demonstrate several properties of the defect and prove an explicit formula for the defect of the Fourier matrix FN of size N. In this way we obtain an upper bound for the dimension of a smooth orbit of inequivalent unitary complex Hadamard matrices stemming from FN. It is equal to zero iff N is prime and coincides with the dimension of the known orbits if N is a power of a prime. Two constructions of these orbits are presented at the end of this work.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issues 2–3, 15 July 2008, Pages 447-481